Purchase this Material for $10

You need to sign up or log in to purchase.

Subscribe for All Access
You need to sign up or log in to purchase.

Solutions
45 Videos

For each angle, use exact values to show that `sin^2 x + cos^2 x = 1`

.

`x = 60^{\circ}`

Buy to View

Q1a

For each angle, use exact values to show that `sin^2 x + cos^2 x = 1`

.

`x = 150^{\circ}`

Buy to View

Q1b

For each angle, use exact values to show that `sin^2 x + cos^2 x = 1`

.

`x = 225^{\circ}`

Buy to View

Q1c

Determine the exact value of each expression.

`sin 45^{\circ} \times tan 30^{\circ} \times cos 120^{\circ}`

Buy to View

Q2a

Determine the exact value of each expression.

`sin 240^{\circ} + tan 225^{\circ} - cos 330^{\circ}`

Buy to View

Q2b

Determine the exact value of each expression.

`sin 270^{\circ} \times tan 300^{\circ} - cos 180^{\circ}`

Buy to View

Q2c

A guy wire is fastened 6 m from the base of a flagpole and makes an angle `\theta`

with the ground. For each given angle `\theta`

, determine

i) the length of the wire

ii) how far up the pole the wire is fastened

`45^{\circ}`

Buy to View

Q3a

A guy wire is fastened 6 m from the base of a flagpole and makes an angle `\theta`

with the ground. For each given angle `\theta`

, determine

i) the length of the wire

ii) how far up the pole the wire is fastened

`30^{\circ}`

Buy to View

Q3b

A guy wire is fastened 6 m from the base of a flagpole and makes an angle `\theta`

with the ground. For each given angle `\theta`

, determine

i) the length of the wire

ii) how far up the pole the wire is fastened

`60^{\circ}`

Buy to View

Q3c

A tiling company develops a floor tile in the shape of a regular hexagon that has an area of `30 cm^2`

. Determine the exact length of the six equal sides of the tile.

Buy to View

Q4

The coordinates of a point on the terminal arm of an angle `\theta`

are shown. Determine the exact trigonometric ratios for `\theta`

.

E(-5, 12)

Buy to View

Q5a

The coordinates of a point on the terminal arm of an angle `\theta`

are shown. Determine the exact trigonometric ratios for `\theta`

.

F(8, -6)

Buy to View

Q5b

One of the primary trigonometric ratios for an angle is given, as well as the quadrant in which the terminal arm lies. Find the other two primary trigonometric ratios.

`sin G = -\dfrac{5}{11}`

, third quadrant

Buy to View

Q6a

One of the primary trigonometric ratios for an angle is given, as well as the quadrant in which the terminal arm lies. Find the other two primary trigonometric ratios.

`cos E = \dfrac{4}{7}`

, first quadrant

Buy to View

Q6b

Solve each equation for `0^{\circ} \leq \theta \leq 360^{\circ}`

.

`sin \theta = \dfrac{5}{8}`

Buy to View

Q7a

Solve each equation for `0^{\circ} \leq \theta \leq 360^{\circ}`

.

`cos \theta = -0.35`

Buy to View

Q7b

Solve each equation for `0^{\circ} \leq \theta \leq 360^{\circ}`

.

`tan \theta = \dfrac{4}{9}`

Buy to View

Q7c

Determine exact expressions for the six trigonometric ratios for `120^{\circ}`

.

Buy to View

Q8

Each point lies on the terminal arm of an angle in standard position. Determine exact expressions for the six trigonometric ratios for each angle.

T(24, -7)

Buy to View

Q9a

Each point lies on the terminal arm of an angle in standard position. Determine exact expressions for the six trigonometric ratios for each angle.

U(-5, -3)

Buy to View

Q9b

Each point lies on the terminal arm of an angle in standard position. Determine exact expressions for the six trigonometric ratios for each angle.

V(4, -9)

Buy to View

Q9c

W(1, 3)

Buy to View

Q9d

For each triangle, determine the number of solutions then solve the triangle if possible.

In `\triangle ABC`

, `\angle A = 71^{\circ}`

, a = 12.2 m, and b = 11.4 m.

Buy to View

Q10a

For each triangle, determine the number of solutions then solve the triangle if possible.

In `\triangle ABC`

, `\angle A = 55^{\circ}`

, a = 7.1 cm, and b = 9.6 cm.

Buy to View

Q10b

For each triangle, determine the number of solutions then solve the triangle if possible.

In `\triangle ABC`

, `\angle A = 44^{\circ}`

, a = 9.3 mm, and b = 12.3 mm.

Buy to View

Q10c

For each triangle, determine the number of solutions then solve the triangle if possible.

In `\triangle DEF`

, `\angle D = 42^{\circ}`

, d = 8.5 km, and f = 7.3 km.

Buy to View

Q10d

For each triangle, determine the number of solutions then solve the triangle if possible.

In `\triangle DEF`

, `\angle E = 38^{\circ}`

, d = 16.6 mm, and e = 13.4 mm.

Buy to View

Q10e

For each triangle, determine the number of solutions then solve the triangle if possible.

In `\triangle DEF`

, `\angle D = 47^{\circ}`

, d = 8.1 m, and f = 12.2 m.

Buy to View

Q10f

A marathon swimmer starts at Island A, swims 9.2 km to Island B, then 8.6 km to Island C. The angle formed by a line from Island B to Island A and a line from Island C to Island A is `52^{\circ}`

. How far does the swimmer have to swim to return directly to Island A?

Buy to View

Q11

A solar-heated house is 10 m wide. The south side of the roof, containing the solar collectors, rises for 8 m at an angle of elevation of `60^{\circ}`

.

a) Determine the length of the north side of the roof.

b) At what angle of elevation does the north side of the roof rise?

Buy to View

Q12a

The pilot of a hot-air balloon, flying above a bridge, measures the angles of depression to each end of the bridge to be `54^{\circ}`

and `71^{\circ}`

. The direct distance from the balloon to the nearer end of the bridge is 270 m. Determine the length of the bridge.

Buy to View

Q13

`54^{\circ}`

and `71^{\circ}`

. The direct distance from the balloon to the nearer end of the bridge is 270 m. Determine the length of the bridge.

Buy to View

Q13

Two roads intersect at an angle of `34^{\circ}`

. Car A leaves the intersection on one of the roads and travels at 80 km/h. At the same time, Car B leaves the intersection on the other road and travels at 100 km/h. Two hours later a reporter in a traffic helicopter, which is above and between the two cars, notes that the angle of depression to the slower car is `20^{\circ}`

and that the helicopter is 1 km from that vehicle. How far is the faster car from the helicopter?

Buy to View

Q14

The port of Math Harbour is located 200 km from Trig Town Inlet in a direction `50^{\circ}`

east of north. A yacht leaves Trig Town Inlet at 8:00 am. and sails in a direction `15^{\circ}`

west of north at a speed of 15 km/h. At the same time, a fishing boat leaves Math Harbour on a course `80^{\circ}`

west of south at a speed of 20 km/h. Determine the distance, to the nearest kilometre, between the yacht and the fishing boat at 1:00 pm.

Buy to View

Q15

State an equivalent expression for each.

`cos^2 \theta`

Buy to View

Q16a

State an equivalent expression for each.

`csc^2 \theta`

Buy to View

Q16b

State an equivalent expression for each.

`cot^2 \theta`

Buy to View

Q16c

State an equivalent expression for each.

`sec^2 \theta - 1`

Buy to View

Q16d

State an equivalent expression for each.

`sec^2 \theta - tan^2 \theta`

Buy to View

Q16e

State an equivalent expression for each.

`\dfrac{1}{sec^2 \theta}`

Buy to View

Q16f

Prove each identity.

`sec^2 \theta + csc^2 \theta = (tan \theta + cot \theta)^2`

Buy to View

Q17a

Prove each identity.

`\dfrac{sin \theta + cos \theta cot \theta}{cot \theta} = sec \theta`

Buy to View

Q17b

Prove each identity.

`sin^2 \theta = cos \theta (sec \theta - cos \theta)^2`

Buy to View

Q17c

Prove each identity.

`\dfrac{1}{1 + cos \theta} = csc^2 \theta - \dfrac{cot \theta}{sin \theta}`

Buy to View

Q17d

Prove each identity.

`\dfrac{1 + csc \theta}{cot \theta} - sec \theta = tan \theta`

Buy to View

Q17e