Question

-Draw the given angle in standard position.-Find and label the reference angle.-Determine the exact values for the sides of the triangle formed with the reference angle and the x-axis with the value of the hypotenuse as 1. -Label the sides on picture of your triangle right out the exact answer to each of the six trig functions.
`0 = (4\pi)/(3)`determine the exact values for:
`\sin0 =`
`\cos0 =`
`\tan0 =`
`\csc = 0`
`\sec = 0`
`\cot0 =`

Answer 1

Question:

Solution:

Remember the trigonometric circle (unit circle):

Remember that in this circle, the y-coordinates are the sine functions and the x-coordinates are the cosine functions. Thus, notice that 3pi/4 is 135 degrees, and :

`\cos \text{ (}(3\pi)/(4)\text{)}=\text{ x - coordinate =- }\frac{\sqrt[]{2}}{2}`

`\sin \text{ (}(3\pi)/(4)\text{)}=\text{ y - coordinate = }\frac{\sqrt[]{2}}{2}`
`\tan \text{(}(3\pi)/(4)\text{)}=\text{ }(\sin ((3\pi)/(4)))/(\cos ((3\pi)/(4)))=\text{ -1}`
`cot\text{(}(3\pi)/(4)\text{)}=\text{ }(\cos ((3\pi)/(4)))/(\sin ((3\pi)/(4)))=\text{ -1}`
`\csc \text{ (}(3\pi)/(4)\text{)}=\text{ }(1)/(\sin ((3\pi)/(4)))=\frac{2}{\sqrt[]{2}}`
`\sec \text{ (}(3\pi)/(4)\text{)}=\text{ }(1)/(\cos ((3\pi)/(4)))=-\frac{2}{\sqrt[]{2}}`