Draw the reference triangle on the unit circle

Reference no: EM132728582

Trigonometry assignment

1. For t = -10, draw the reference triangle on the unit circle, and give approximate values for cos( -10) and sin( -10).

2. Graph the following function by 'framing', find and using the vertical shift, phase shift, period, and amplitude:

f (t) = 2 - 4 sin (t + 1) .

3. Find an approximate formula for the graph below, showing all of your work:

4. Give all distances t, approximately, for which

(a) cos(t) = -0.9
(b) tan(t)=2

5. Draw a right triangle, with all three sides given exactly, with cos( α) = 0.15, and with a = 10.

6. (a.) How long exactly the arc on a circle of radius 7 cm that is subtended by an angle of 37° ?

(b) What is the angular velocity of a particle that is going around a circle of radius 7 cm, at the rate of 45 revolutions per minute?

7. If

- sin(t1) = -0.2 and t1 lies in the third quadrant, and
- tan(t2)= 8 and t 2 lies in the first quadrant, find

(a) the exact value of sin(2t2)

(b) the exact value of cos( 1/2 t1)
(c) the exact value of cos(t1 + t 2)
(d) Check your answer to (c) by approximating t1 and t 2 using the unit circle, and plugging that value into the cosine function.

Reference no: EM132728582

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