SOLUTION: Evaluate the expression. sin(90-theta)*tan(theta)*sec(theta) a)sin(theta) b)cos(theta) c)tan(theta) d)cot(theta) (Homeschooling mother. Any help is appreciated. Thank y

Algebra ->  Trigonometry-basics -> SOLUTION: Evaluate the expression. sin(90-theta)*tan(theta)*sec(theta) a)sin(theta) b)cos(theta) c)tan(theta) d)cot(theta) (Homeschooling mother. Any help is appreciated. Thank y      Log On


   



Question 1103427: Evaluate the expression.
sin(90-theta)*tan(theta)*sec(theta)
a)sin(theta)
b)cos(theta)
c)tan(theta)
d)cot(theta)
(Homeschooling mother. Any help is appreciated. Thank you)

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


sin%2890-x%29+=+cos%28x%29

You can see this if you think of a right triangle. In a right triangle, the acute angles are x and 90-x; by the basic definition of the functions in a right triangle, the sine of one acute angle is the cosine of the other, and vice versa. So sin(90-x) = cos(x) and cos(90-x) = sinx.

Then, by definition, tan%28x%29+=+sin%28x%29%2Fcos%28x%29 and sec%28x%29+=+1%2Fcos%28x%29

So


Answer c.