### Home > A2C > Chapter 8 > Lesson 8.1.7 > Problem8-105

8-105.

Evaluate each of the following trig expressions without using a calculator. Homework Help ✎

1. $\sin(180^\circ)$

Every point on the unit circle is defined as $(\cosθ,\sinθ)$.
Where is $180^\circ$ on the unit circle?
Where is the $y-$value at that point?

$0$

1. $\sin(360^\circ)$

See part (a).

1. $\sin(−90^\circ)$

When an angle is negative, it opens clockwise from $0^\circ$ on the unit circle.

1. $\sin(510^\circ)$

Find an equivalent angle between $0^\circ\ \text{and}\ 360^\circ$ by subtracting $510 − 360$. Notice that the reference triangle is a $30^\circ-60^\circ-90^\circ$ triangle. Find the $\sin30^\circ$.

$0.5$

1. $\cos(90^\circ)$

What is the $x-$value in this location?

$0$

1. $\tan(−90^\circ)$

Remember the tangent is the ratio of $\frac{y}{x}$.

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