SOLUTION: What happens to cos θ as θ approaches 90 degrees? Why? What happens to sin θ as θ approaches 90 degrees? Why? What happens to tan θ as θ approaches 90 degrees? Why?

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Question 1185158: What happens to cos θ as θ approaches 90 degrees? Why?
What happens to sin θ as θ approaches 90 degrees? Why?
What happens to tan θ as θ approaches 90 degrees? Why?
Answer by MathLover1(20855) About Me  (Show Source):
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What happens to cos%28theta%29 as theta approaches 90 degrees? Why?
answer: Right -angled triangle!
All triangles have 3 angles that add to 180 degrees. Therefore, if one angle is 90 degrees we can figure out sin%28theta%29+=+cos+%2890+-%28theta%29%29 and cos+%28theta%29+=+sin+%2890+-+%28theta%29%29.

cos


What happens to sin%28theta%29 as theta approaches 90 degrees? Why?
As the angle approaches 90 degrees, the triangle will be compressed horizontally and the cosine approaches zero.
sin


What happens to tan%28theta%29 as theta approaches 90 degrees? Why?
At zero degrees this tangent length will be zero. Hence, tan%28theta%29=0. As our first quadrant angle increases, the tangent will increase very rapidly. As we get closer to 90+degrees, this length will get incredibly large. At 90 degrees we must say that the tangent is undefined, because when you divide the leg opposite by the leg adjacent you cannot divide by zero.
tan