Trignomoetric Functions

Question

Find a possible formula of the form A sin x+ k or B cos x + k for the trigonometric function whose values are in the following table:

x 0, π/2, π

g(x) 3.5, 0.8 , −1.9

Answer 1

Whether g(x) = A sin(x) + k or g(x) = B cos(x) + k,

just the two given values g(0) and g(π/2) are sufficient to determine the unknown coefficients.

Then we can use the given g(π) for a check.

Case 1: g(x) = A sin(x) + k

Determine k:

g(0) = A sin(0) + k

3.5 = k

Determine A:

g(π/2) = A sin(π/2) + k

0.8 = A + 3.5

A = -2.7

Check:

g(π) = A sin(π) + k

-1.9 = + 3.5

Therefore Case 1 does not work.

Case 2: g(x) = B sin(x) + k

Determine k:

g(π/2) = B cos(π/2) + k

0.8 = k

Determine B:

g(0) = B cos(0) + k

3.5 = B + 0.8

B = 2.7

Check:

g(π) = B cos(π) + k

-1.9 = 2.7 x (-1) + 0.8

-1.9 = -1.9

Therefore g(x) = 2.7 cos(x) + 0.8 fits the data.