Question 1185157



What happens to {{{cos(theta)}}} 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(theta) = cos (90 -(theta))}}} and {{{cos (theta) = sin (90 - (theta))}}}.


<a href="https://ibb.co/LPRgVKQ"><img src="https://i.ibb.co/LPRgVKQ/cos.png" alt="cos" border="0"></a>



What happens to {{{sin(theta)}}} as {{{theta}}} approaches {{{90}}} degrees? Why?

As the angle approaches 90 degrees, the triangle will be compressed horizontally and the cosine approaches {{{zero}}}.

<a href="https://ibb.co/Jn4G7hW"><img src="https://i.ibb.co/Jn4G7hW/sin.png" alt="sin" border="0"></a>



What happens to {{{tan(theta)}}} as {{{theta}}} approaches {{{90}}} degrees? Why?

At zero degrees this tangent length will be zero. Hence, {{{tan(theta)=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.

<a href="https://ibb.co/zNM7NDc"><img src="https://i.ibb.co/zNM7NDc/tan.png" alt="tan" border="0"></a>