Question

If sin θ = 3/8 and θ is in the second quadrant, find values of all 5 other trigonometric functions of θ

Answer 1

Hence The other five trigonometric function as :

CosФ =
`(√(73))/(8)`

TanФ =
`(3)/(√(73))`

SecФ =
`(8)/(√(73))`

CotФ =
`(√(73))/(3)`

Explanation:

Given as :

sin Ф =
`(3)/(8)`

∵ sin Ф =
`(perpendicular)/(hypotenuse)`

So,
`(perpendicular)/(hypotenuse)` =
`(3)/(8)`

Then from Pythagorean theorem

Hypotenuse² = Perpendicular² + Base²

So, Base² = Hypotenuse² - Perpendicular²

Or, Base² = 8² + 3² = 64 + 9 = 73

∴ Base = √73

So, CosФ =
`(Base)/(hypotenuse)`

CosФ =
`(√(73))/(8)`

TanФ =
`(perpendicular)/(Base)`

TanФ =
`(3)/(√(73))`

SecФ =
`(hypotenuse)/(base)`

SecФ =
`(8)/(√(73))`

CotФ =
`(Base)/(Perpendicular)`

CotФ =
`(√(73))/(3)`

CosecФ =
`(hypotenuse)/(perpendicular)`

CosecФ =
`(8)/(3)`

Hence The other five trigonometric function as :

CosФ =
`(√(73))/(8)`

TanФ =
`(3)/(√(73))`

SecФ =
`(8)/(√(73))`

CotФ =
`(√(73))/(3)`

CosecФ =
`(8)/(3)` Answer