Draw the reference triangle on the unit circle

Question

Assignment Problem: Trigonometry

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

Question 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).

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

Question 4: Give all distances t, approximately, for which

(a) cos(t) = -0.9

(b) tan(t)=2

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

Question 6:

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

(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?

(c) What is the linear velocity of that same particle?

Question 7: If sin(t₁) = -0.2 and t1 lies in the third quadrant, and tan(t₂)= 8 and t₂ lies in the first quadrant, find

(a) The exact value of sin(2t₂)

(b) The exact value of cos(1/2t₁)

(c) The exact value of cos(t₁+t₂)

(d) Check your answer to (c) by approximating t1 and t2 using the unit circle, and plugging that value into the cosine function.

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