https://file.aiquickdraw.com/mathbot/file/1730165590109187298hr.jpg

Let's work through each problem on this trigonometry worksheet.

---

### Problem 1
Given:
- \( A \) is in quadrant II, and \( \sin A = \frac{7}{8} \).
- Find \( \cos A \).

In quadrant II, \( \cos A \) is negative. Using the Pythagorean identity:
\[
\sin^2 A + \cos^2 A = 1
\]
\[
\left(\frac{7}{8}\right)^2 + \cos^2 A = 1
\]
\[
\frac{49}{64} + \cos^2 A = 1
\]
\[
\cos^2 A = 1 - \frac{49}{64} = \frac{15}{64}
\]
\[
\cos A = -\frac{\sqrt{15}}{8}
\]
The correct answer is **d.** \( -\frac{\sqrt{15}}{8} \).

---

### Problem 2
Evaluate:
\[
\frac{\sin 120^\circ - \cos 225^\circ}{\tan 60^\circ}
\]

We know:
- \( \sin 120^\circ = \frac{\sqrt{3}}{2} \)
- \( \cos 225^\circ = -\frac{\sqrt{2}}{2} \)
- \( \tan 60^\circ = \sqrt{3} \)

Substitute these values:
\[
\frac{\frac{\sqrt{3}}{2} - \left(-\frac{\sqrt{2}}{2}\right)}{\sqrt{3}}
\]
\[
= \frac{\frac{\sqrt{3} + \sqrt{2}}{2}}{\sqrt{3}} = \frac{\sqrt{3} + \sqrt{2}}{2\sqrt{3}}
\]

This simplifies to **answer b**.

---

### Problem 3
For a right triangle, given \( \sin A = \frac{2}{3} \), find \( \cos B \).

---

Would you like detailed explanations for all solutions? Here are further questions for practice:

1. How do you determine the sign of trigonometric functions in different quadrants?
2. What is the Pythagorean identity, and how is it applied in trigonometry?
3. How can you simplify trigonometric expressions with square roots?
4. Why does the cosine function have a negative value in the second quadrant?
5. What are the values of common trigonometric functions for specific angles like \(120^\circ\), \(225^\circ\), etc.?

**Tip:** Memorizing key angle values for trigonometric functions helps simplify calculations significantly.

This page contains a trigonometry worksheet with multiple-choice questions covering quadrants, trigonometric identities, and the evaluation of trigonometric functions for specific angles. Ideal for students in Grades 10-12, this worksheet focuses on calculating values like sin and cos in different quadrants, applying the Pythagorean identity, and using trigonometric ratios.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation