Question

Find the exact trigonometric ratios for the angle x whose radian measure is given. (if an answer is undefined, enter undefined.) 3π 4

Answer 1

Angle x = 3 π / 4 = 135°
The angle is in the 2nd Quadrant.
Answer:
sin x = √2 / 2
cos x = - √2/ 2
tan x = - 1
cot x = - 1. 

Answer 2

Trigonometric ratios value for the angle

$sin\frac{\pi }{4}=\frac{1}{2} \sqrt{2}$

$cos\frac{\pi }{4}=-\frac{1}{2} \sqrt{2}$

$tan\frac{\pi }{4}=-1$

$cot\frac{\pi }{4}=-1}$

$sec\frac{\pi }{4}=-\sqrt{2}$

$csc\frac{\pi }{4}=\sqrt{2}$

Further explanation

The angle of a triangle expressed in trigonometric ratios

The angle can change from 0° to 360°

In the Cartesian field, there are 4 regions called quadrants.

• 1. quadrant 1: 0 <a <90
• 2. quadrant 2: 90 <a <180
• 3. quadrant 3: 180 <a <270
• 4. quadrant 4: 279 <a <360

In this quadrant, the positive angle is (meaning another angle will be  negative value)

• 1. quadrant 1: all angles
• 2. quadrant 2: sin and csc
• 3. quadrant 3: tan and cot
• 4. quadrant 4: cos and sec

The angle x with an angle of 3/4π

$\frac{3}{4}\pi=(\pi-\frac{1}{4}\pi)=\frac{\pi }{4}$

The angle x is in quadrant 2, so the angle that is positive value is only sin and csc

Then the exact trigonometric ratios value for the angle

$sin\frac{\pi }{4}=\frac{1}{2} \sqrt{2}$

$cos\frac{\pi }{4}=-\frac{1}{2} \sqrt{2}$

$tan\frac{\pi }{4}=-1$

$cot\frac{\pi }{4}=-1}$

$sec\frac{\pi }{4}=-\sqrt{2}$

$csc\frac{\pi }{4}=\sqrt{2}$

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Keywords: quadrant, trigonometry, angle, ratios