Use common trigonometric identities for the functions given to find the indicated trigonometric functions.?

Question

Use common trigonometric identities for the functions given to find the indicated trigonometric functions. (Hint: Remember the reciprocal properties of sine, cosine, and tangent.) Show all work to receive full credit. Give answers in exact form – no decimals.

A. If sin 30 degrees = 1/2 and cos 30degrees = radical 3 over2 , what are the values of

a) = tan 30 degrees

b) =csc30 degrees

c) =cot 30 degrees

B. If sec (there is an 0 with a line throughit) = 3 and tan (the sane 0) = 2 radical 2, what are the values of

a) =cot (same 0)

b) =sin (same 0)

c) =cos^2 (same 0 with a line through it)

Answer 1

A(a)

tan(30) = sin(30) / cos(30)

= (1 / 2) / (sqrt(3) / 2)

= 1 / sqrt(3) or sqrt(3) / 3.

(b)

csc(30) = 1 / sin(30)

= 2.

(c)

cot(30) = 1 / tan(30)

= sqrt(3).

B.

sec(theta) = 3

tan(theta) = 2 sqrt(2)

(a)

cot(theta) = 1 / tan(theta)

= 1 / [ 2 sqrt(2) ]

= sqrt(2) / 4.

(c)

cos(theta) = 1 / sec(theta)

= 1 / 3

cos^2(theta) = 1 / 9.

(b)

sin(theta) / cos(theta)

= tan(theta)

= 2 sqrt(2)

Using cos(theta) = 1 / 3 from (c):

sin(theta) = 2 sqrt(2) / 3.