If the measure of angle ø is 3pie/4, which statements are true?
The measure of the reference angle is 45°.
cos (0) = √2
sin (0) = √2
The measure of the reference angle is 60°.
The measure of the reference angle is 30°.
tan (0) = 1

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]

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