Topic THREE

Trig Ratios

100

Given that right triangle ABC with B as a right angle, find x (rounded to the nearest whole number), and then find the measure of each unknown angle, if AC is 13 cm and BC is 11 cm.

132-112=x2 169-121 = 48 x=7 Angle C = sin-1(7/13) = 32.6 degrees Angle A = cos-1(7/13) = 57.4 degrees

200

Given cos x = 8/11, and x is acute, find sin 2x without finding x.

112-82=a2 121-64=57 a=7.55 sin x = 7.55/11 sin-1(7.55/11)=43.3 degrees sin 2(43.3 degrees) = .998

300

Given sinθ = √(8)/4, find tanθ without finding θ.

sin θ = O/H tan θ = √(8)/A 42-√(8)2=8 A=√(8) tan θ = √(8)/ √(8)

400

Find the value of x in trapezoid LMNO, given that the measure of angle L is 55°, the measure of angle O is 70°, and NO=6 m:

sin 70 = y/6 m 6(sin(70)) = y y = 5.63 m sin 55 = 5.63 m/x x sin 55 = 5.63 m x = 5.63 m/sin 55 x = 6.87 m

500

Find the angle of elevation to the top of a mountain 2500 m high from a point 6.048 km from its base.

tan E = 2.5/6.048 tan-1(2.5/6.048) = 22.5 degrees

Unit Circle

100

At an angle of 45 degrees, estimate sinθ and cosθ.

.707 and .707

200

At an angle of 179 degrees, estimate sinθ and cosθ.

.017 and -1.00

300

Draw and Label a Unit Circle

See sheet.

400

Using a unit circle, find cos(-π/2) and sin(-π/2)

(0,-1)

500

If sinθ= (-3/4) and π<θ<(3π/2) find cosθ without using a calculator

cosθ=-√7/4

Triangle Trig

100

Find the area of the non-right triangle and the length of side x.

Answer: A= 79.5 units squared x = 14.1

200

Find the length of side x.

Answer: x: 24.1

300

Billy wants to determine the height of a flag pole. He takes a sighting of the top of the flag pole from point P. He then movies further away from the flagpole by 20 metres to point Q and takes a second sighting. How high is the flag pole. (hint: elevation and depression)

Answer: h = 17.7

400

Given that the radius is 12 cm and the angle at center is 125o. Find the area of the shaded region.

98.08cm2

500

Find the area and the perimeter of the sector of a circle of radius 23.6 cm if the angle at the center is 115 degrees.

Area of the sector, (115/360)π23.6 2 = 558.9 cm2 Perimeter=94.57 cm

Periods

100

Convert to radians in terms of π A=90 degrees

π/2

200

In the equation y=AsinB(x-C)+D, what does B do?

Affects the period

300

Simplify: 2cosθ-5cosθ

-3cosθ

400

Factor: (sin^2)θ+5sinθ+6

(sinθ+3)(sinθ+2)

500

In terms of π only, solve tan4x=√3. Find exact answers

x=π/12+(π/4)k