Simplify the following without the use of a calculator:
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter2: Right Triangle Trigonometry
Section: Chapter Questions
Problem 6GP
Related questions
Question
![### Question 2
#### Instruction:
Simplify the following without the use of a calculator:
#### Sub-questions:
2.1
\[
\frac{\cos(90°-x) \cdot \sin(-x)}{\cos^2(180°+x)}
\]
2.2
\[
\frac{\sin(360°-x) \cdot \tan(-x)}{\cos(180°+x) \cdot (\sin^2A + \cos^2A)}
\]
2.3
\[
\frac{\sin 210° \cdot \cos 400°}{\sin(-50°) \cdot \cos 120°}
\]
2.4
\[
\frac{\cos 210° \cdot \tan 135°}{\sin(-60°) \cdot \cos 420°}
\]
### Question 3
#### Instruction:
In the diagram below,
1. \(CBD = 44°\)
2. \(DBE = 20°\)
3. \(BC = 20cm\)
4. \(B\widehat{C}D = 90°\)
#### Diagram:
The diagram illustrates a geometric figure with points labeled B, C, and D forming a right triangle with \(\angle BCD = 90°\). Side BC has a length of 20 cm. Angle CBD is given as 44° and angle DBE is given as 20°. The notation and angle measurements are clearly marked on the diagram.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55de4ee6-b3c5-48b2-9cae-ebf8052fd740%2F16bc10b5-f000-412f-8855-23cf62a87ab6%2Fn1bi3a8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 2
#### Instruction:
Simplify the following without the use of a calculator:
#### Sub-questions:
2.1
\[
\frac{\cos(90°-x) \cdot \sin(-x)}{\cos^2(180°+x)}
\]
2.2
\[
\frac{\sin(360°-x) \cdot \tan(-x)}{\cos(180°+x) \cdot (\sin^2A + \cos^2A)}
\]
2.3
\[
\frac{\sin 210° \cdot \cos 400°}{\sin(-50°) \cdot \cos 120°}
\]
2.4
\[
\frac{\cos 210° \cdot \tan 135°}{\sin(-60°) \cdot \cos 420°}
\]
### Question 3
#### Instruction:
In the diagram below,
1. \(CBD = 44°\)
2. \(DBE = 20°\)
3. \(BC = 20cm\)
4. \(B\widehat{C}D = 90°\)
#### Diagram:
The diagram illustrates a geometric figure with points labeled B, C, and D forming a right triangle with \(\angle BCD = 90°\). Side BC has a length of 20 cm. Angle CBD is given as 44° and angle DBE is given as 20°. The notation and angle measurements are clearly marked on the diagram.
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