Let's solve the questions one by one based on the graph and table provided.

Question 91: Referring to Figure 1, tan(160°) = ?

Solution:

1. From the figure, $160^\circ$ lies in the second quadrant. In this quadrant, the tangent function ($\tan$) is negative.

2. The reference angle for $160^\circ$ is $180^\circ - 160^\circ = 20^\circ$.

3. Using the formula: $\tan(160^\circ) = -\tan(20^\circ)$

4. Among the options, $\tan(160^\circ) = -\tan(20^\circ)$ matches.

Answer: $-\tan(20^\circ)$

Question 92: Referring to Figure 1, sin(−120°) = ?

Solution:

1. The angle $-120^\circ$ means a clockwise rotation of $120^\circ$, which places it in the third quadrant.

2. In the third quadrant, the sine function ($\sin$) is negative.

3. The reference angle for $-120^\circ$ is $180^\circ - 120^\circ = 60^\circ$.

4. Using the formula: $\sin(-120^\circ) = -\sin(60^\circ)$

5. Among the options, $\sin(-120^\circ) = -\sin(60^\circ)$ matches.

Answer: $-\sin(60^\circ)$

Question 93: $\frac{\pi}{2}$ radians = ?

Solution:

1. To convert radians to degrees, use the formula: $\text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi}$

2. Substituting $\frac{\pi}{2}$: $\text{Degrees} = \frac{\pi}{2} \times \frac{180^\circ}{\pi} = 90^\circ$

3. Among the options, $\frac{\pi}{2}$ radians corresponds to $90^\circ$.

Answer: $90^\circ$

Question 94: $150^\circ = ?$ (in radians)

Solution:

1. To convert degrees to radians, use the formula: $\text{Radians} = \text{Degrees} \times \frac{\pi}{180^\circ}$

2. Substituting $150^\circ$: $\text{Radians} = 150^\circ \times \frac{\pi}{180^\circ} = \frac{5\pi}{6}$

3. Among the options, $150^\circ = \frac{5\pi}{6}$.

Answer: $\frac{5\pi}{6}$

Question 95: If $\sin(x) = -1$, then $x = ?$

Solution:

1. The sine function ($\sin(x)$) equals $-1$ at $x = 3\pi/2$ radians (or $270^\circ$).

2. This happens because at $x = 3\pi/2$, the point on the unit circle is $(0, -1)$, where the $y$-coordinate represents $\sin(x)$.

3. Among the options, $x = \frac{3\pi}{2}$.

Answer: $\frac{3\pi}{2}$

Recap of Answers:

• 91: $-\tan(20^\circ)$
• 92: $-\sin(60^\circ)$
• 93: $90^\circ$
• 94: $\frac{5\pi}{6}$
• 95: $\frac{3\pi}{2}$

Would you like further details or have any questions?

Here are 5 related questions to practice:

1. What is the value of $\tan(120^\circ)$?
2. Convert $45^\circ$ to radians.
3. In which quadrants is the sine function positive?
4. What is the reference angle for $210^\circ$?
5. If $\cos(x) = -1$, what is $x$?

Tip: Always identify the quadrant of the angle first, as it determines the sign of the trigonometric functions!