Respuesta :
Find 3π/4 in degrees
- (3(180))/4
- 3(45)
- 135°
Referance angle
- π-3π/4
- 180-135
- 45° or π/4
Option A
- TanØ=sinØ/cosØ=√2/√2=1
Answer:
The measure of the reference angle is 45°.
[tex]\sin(\theta)=\dfrac{\sqrt{2}}{2}[/tex]
Step-by-step explanation:
Reference Angle: The smallest possible angle made by the terminal side of the given angle and the x-axis. The reference angle is always between 0° and 90° (0 and π/2 radians).
To convert radians to degrees, multiply by 180/π:
[tex]\implies \sf \theta=\dfrac{3\pi}{4} \cdot \dfrac{180}{\pi}=135^{\circ}[/tex]
Positive angles are drawn in a counterclockwise direction from the x-axis.
(See attached for diagram of the angle θ and its reference angle).
Angles on a straight line sum to 180°.
Therefore, to calculate the reference angle, subtract the measure of the angle from 180°:
[tex]\implies \sf Reference\:angle=180^{\circ}-135^{\circ}=45^{\circ}[/tex]
The angle 135° lies between 90° and 180° and so is in Quadrant II.
Therefore, the exact trigonometric ratios for 135° are:
[tex]\sin 135^{\circ}=\dfrac{1}{\sqrt{2}} \textsf{ or }\dfrac{\sqrt{2}}{2}\\\\ \textsf{(Since sine function is positive in the Quadrant II)}[/tex]
[tex]\cos 135^{\circ}=-\dfrac{1}{\sqrt{2}} \textsf{ or }-\dfrac{\sqrt{2}}{2}\\\\\textsf{(Since cosine function is negative in the Quadrant II)}[/tex]
[tex]\tan135^{\circ}=-1\\\\\textsf{(Since tangent function is negative in the Quadrant II)}[/tex]
Therefore, the true statements are:
The measure of the reference angle is 45°.
[tex]\sin(\theta)=\dfrac{\sqrt{2}}{2}[/tex]
