Diagnostic Test D Trigonometry This is a take home Quiz due

Diagnostic Test [D]: Trigonometry

(This is a take home Quiz due tommorow so make sure to answer the questions correctly and show all work, thanks!)

1. Convert from degrees to radians.

a. 300 degrees

b. -18 degrees

2. Convert from radians to degrees.

a. 5/6

b. 2

3. Find the length of an arc of a circle with radius 12 cm if the arc subtends a central angle of 30 degrees.

4. Find the exact values

a. Tan(/3)

b. Sin(7/6)

c. Sec(5/3)

5. Express the lengths a and b in the figure in terms of .

(The figure is a right triangle with a hypotenuse of 24 and unknown sides a and b. The unknown angle is across from side a. The triangle points to the left and side a is on the right.)

6. If sin x=1/3 and sec y=5/4, where x and y lie between 0 and /2, evaluate sin(x+y).

7. Prove the identities.

a. Tan sin= + cos = sec

b. 2tanx/ (1 + tan²x) = sin 2x

8. Find all values of x such that sin 2x = sin x and 0 x 2.

9. Sketch the graph of the function y = 1 + sin 2x without using a calculator

Solution

1 a) convert from degrees to radians

we know : 180deg = pi radians

pi = 3.18 (approx)

a) 300 deg

300deg = (pi/180)*360 = 2pi = 6.28 rad

b) -18 deg:

-18deg = (pi/180)*(-18) = -pi/10 = -0.318 rad

2. radians to degrees.

we know : pi radians = 180deg

a. 5/6

So,5/6 = (180/)*(5/6) = 150 deg

b. 2

So, 2 = ((180/)*2 = 282.75 deg

3. length of an arc of a circle with radius 12 cm if the arc subtends a central angle of 30 degrees.

360 deg subtends 2**r = 2**12 = 24 com of arc

So, 30 deg would subtebd arc of = (24/360)*30 =2 = 6.28 cm

4. Find the exact values

a. Tan(/3)

= sqrt3

b. Sin(7/6)

sin(pi +pi/6) = -sin(pi/6) =- 1/2

c. Sec(5/3)

= 1/cos(5pi/3)

=1/cos(2pi -pi/3)

= 1/cospi/3

= 2