Question

Cosx=5/8

i) find the exact value of the other five trigonometric functions associated with the angle

ii) use your GDC to find the degree measure of theta and the other acute angle

Answer 1

All the trigonometric ratios are mentioned and the value of x = 51.32°

Explanation:

we are given the value of cosx =
`(5)/(8)`

We have to find all the other 5 trigonometric values.

sinx =
`\sqrt{1-cos^(2)x }` =
`\sqrt{1-((5)/(8))^(2) }`

=
`\sqrt{(39)/(64)} = (√(39))/(8)`

tanx =
`(sinx)/(cosx)` =
`(√(39) )/(5)`

cosecx =
`(8)/(√(39) )`

secx =
`(8)/(5)`

cotx =
`(1)/(tanx)` =
`(5)/(√(39) )`

These are the values of the trigonometric functions.

cosx =
`(5)/(8)`

x =
`cos^(-1) (5)/(8)`

x = 51.32°

The other acute angle = 90 - 51.32 = 38.68°