Trigonometry

5.1 - 5.2

100

What is 'X', in the question, tanX= 4/7 to the nearest degree?

what is 30 degrees

200

What are the formulas for the reciprocal trig ratios?

cesant= 1/sin secant= 1/cos cotangent= 1/tan

300

What is 2cos= √3

30 degrees

400

Suppose that (theta) is an acute angle in a right triangle and sec= 5√3 /4. Find cos, sin and cot.

cos= 4√3/ 15 sin= √177/ 15 cot= 4√59/ 59

500

In right triangle PQR, the hypoteneuse, r, is 117 cm and tanP= 0.51. Calculate the side lengths of p and q and the interior angles to the nearest degrees.

p= 53 cm q= 104 cm Angle P is 27 degrees Angle Q is 63 degrees

5.3 - 5.4

100

State all the angles between 0 degrees and 360 degrees that make the following equation true. Sin45 = Sin ____

135

200

Point (2,-3) lies on the terminal arm of theta in standard position. Find theta and the related acute angle

Related acute angle= 56 degrees Theta= 30 degrees

300

Find the exact value: tan(-210)

Tan 30 = -1 ---- √3

400

The point (6,-8) lies on the terminal arm of theta. state all 3 trig ratios, the related acute angle, and theta.

sin theta = -8/10 cos theta = 6/10 tan theta = -8/6 related acute angle= 53 degrees theta= 307 degrees

500

given cos theta = -5/12, where theta is greater than 0 and less than 360 degrees, in which quadrant would the terminal arm lie?

Quadrant 2 or 3

5.5. - 5.6

100

prove the identity using trig ratios (y,r, and x ) tan theta = sin theta/ cos theta

y/x = tan theta LS = RS

200

Is it possible to sketch: a = 7.3 m, b = 14.6 m,

Yes. A = 30 degrees, a = 7.3 m B = 90 degrees , b = 14,6 m C = 60 degrees , c = 12.6 m

300

prove the identity : sin^2 theta + cos ^2 theta = 1

r^2 = r^2 =1 LS = RS

400

write using sin and cos AND state restrictions csc^2 theta - sec^2 theta

restrictions: 0,90,180,270,360 cos^2theta-sin^2 theta _________________________ sin^2 theta cos^2 theta

500

Prove the identity: (factor) 1 + 1 =2sec^2theta _________ _____________ 1+sin theta 1-sin theta

2/cos^2 theta

5.7 - 5.8

100

Determine unknown side length(j) to the nearest tenth. k = 7.7, l = 11.3,

j = 15.5

200

Determine the value of x to the nearest cm and theta to the nearest degree. Diagram will be given.

15cm

300

25/sin 100 = x/ sin 40 USING SINE LAW FIND X

What is 16

400

As a project, a group of students were asked to determine the altitude, h, of a promotional blimp. The students' measurements are shown in the sketch below. Determine h to the nearest tenth of a metre.

520.5m

500

Two spotlights, one blue and the other white, are placed 6.0 m apart on a track on the ceiling of a ballroom. A stationary observer standing on the ballroom floor notices that the angle of elevation is 45 degrees to the blue spotlight and 70 degrees to the white one. How high, to the nearest tenth of a metre, is the ceiling of the ballroom?

4.4 m

Bonus

100

prove using trig identities (x,y,r): (tan theta )(cos theta ) = sin theta

y/r= y/r

200

Using exact value, show that sin^2 theta + cos^2 theta= 1 for the angle: 45 degrees

(√2/2)^2 + (√2/2)^2 = 1

300

Fill in the blanks. The ambiguous case of the sine law occurs when you know _________.

The ambiguous case of the sine law occurs when you know 2 side lengths and an angle. (SSA)

400

How do you know when to use sine law or cosine law?

Sine law- SSA or ASA or AAS Cosine law- SAS or SSS

500

Determine the exact value of: (sin45 degrees)(cos45 degrees) + (sin30 degrees)(sin60 degrees)

2 + √3 --------- 4