Trigonometric ratios value for the angle
![sin\frac{\pi }{4}=\frac{1}{2} \sqrt{2}](https://tex.z-dn.net/?f=sin%5Cfrac%7B%5Cpi%20%7D%7B4%7D%3D%5Cfrac%7B1%7D%7B2%7D%20%5Csqrt%7B2%7D)
![cos\frac{\pi }{4}=-\frac{1}{2} \sqrt{2}](https://tex.z-dn.net/?f=cos%5Cfrac%7B%5Cpi%20%7D%7B4%7D%3D-%5Cfrac%7B1%7D%7B2%7D%20%5Csqrt%7B2%7D)
![tan\frac{\pi }{4}=-1](https://tex.z-dn.net/?f=tan%5Cfrac%7B%5Cpi%20%7D%7B4%7D%3D-1)
![cot\frac{\pi }{4}=-1}](https://tex.z-dn.net/?f=cot%5Cfrac%7B%5Cpi%20%7D%7B4%7D%3D-1%7D)
![sec\frac{\pi }{4}=-\sqrt{2}](https://tex.z-dn.net/?f=sec%5Cfrac%7B%5Cpi%20%7D%7B4%7D%3D-%5Csqrt%7B2%7D)
![csc\frac{\pi }{4}=\sqrt{2}](https://tex.z-dn.net/?f=csc%5Cfrac%7B%5Cpi%20%7D%7B4%7D%3D%5Csqrt%7B2%7D)
<h3>Further explanation</h3>
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}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%5Cpi%3D%28%5Cpi-%5Cfrac%7B1%7D%7B4%7D%5Cpi%29%3D%5Cfrac%7B%5Cpi%20%7D%7B4%7D)
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}](https://tex.z-dn.net/?f=sin%5Cfrac%7B%5Cpi%20%7D%7B4%7D%3D%5Cfrac%7B1%7D%7B2%7D%20%5Csqrt%7B2%7D)
![cos\frac{\pi }{4}=-\frac{1}{2} \sqrt{2}](https://tex.z-dn.net/?f=cos%5Cfrac%7B%5Cpi%20%7D%7B4%7D%3D-%5Cfrac%7B1%7D%7B2%7D%20%5Csqrt%7B2%7D)
![tan\frac{\pi }{4}=-1](https://tex.z-dn.net/?f=tan%5Cfrac%7B%5Cpi%20%7D%7B4%7D%3D-1)
![cot\frac{\pi }{4}=-1}](https://tex.z-dn.net/?f=cot%5Cfrac%7B%5Cpi%20%7D%7B4%7D%3D-1%7D)
![sec\frac{\pi }{4}=-\sqrt{2}](https://tex.z-dn.net/?f=sec%5Cfrac%7B%5Cpi%20%7D%7B4%7D%3D-%5Csqrt%7B2%7D)
![csc\frac{\pi }{4}=\sqrt{2}](https://tex.z-dn.net/?f=csc%5Cfrac%7B%5Cpi%20%7D%7B4%7D%3D%5Csqrt%7B2%7D)
<h3>Learn more</h3>
trigonometric identities
brainly.com/question/5013374#
trigonometric ratio to find x
brainly.com/question/9880052
trigonometric ratios for triangle XYZ
brainly.com/question/10782297
Keywords: quadrant, trigonometry, angle, ratios