Question

Determine the exact value for each of the 6 trig functions for the point (-2, 6).​

Answer 1

Explanation:

The six trig functions are

`\sin( \alpha ) = (y)/(r)`

`\cos( \alpha ) = (x)/(r)`

`\tan( \alpha ) = (y)/(x)`

`\csc( \alpha ) = (r)/(y)`

`\sec( \alpha ) = (r)/(x)`

`\cot( \alpha ) = (x)/(y)`

Where

`r = \sqrt{ {x}^(2) + {y}^(2) }`

`r = \sqrt{ - 2 {}^(2) + {6}^(2) }`

`r = √(40)`

`r = 2 √(10)`

So we just plug in -2 for x, 6 for y, and our r value into these functions.

`\sin( \alpha ) = (6)/(2 √(10) ) = (3)/( √(10) ) = (3 √(10) )/(10)`

`\cos( \alpha ) = ( - 2)/(2 √(10) ) = ( - 1)/( √(10) ) = ( - √(10) )/(10)`

`\tan( \alpha ) = (6)/( - 2) = - 3`

Csc is the reciprocal of sine.

`\csc( \alpha ) = ( √(10) )/(3)`

Sec is the reciprocal of cosine

`\sec( \alpha ) = - √(10)`

Cot is the reciprocal of tan

`\cot( \alpha ) = - (1)/(3)`

Answer 2

Sine: 0.94

Cosine: -0.31

Cotangent: -0.3(infinite)

Cosecant: 1.05

Tangent: -3

Secant: -3.16

Formula for finding the 6 trigonometry functions

• To find the sine, you must divide the opposite side by the hypotenuse, because the sine is the ratio or fraction whose angle is opposite to the adjacent angle.

• To find a cosine, you must divide the adjacent angle by the hypotenuse.

• When finding a cotangent, you must divide the adjacent angle by the opposite, since the cotangent is also a ratio, but not like a sine.

• When you are finding a cosecant, you divide the hypotenuse by the opposite angle.

• You find the tangent by diving the opposite angle by the adjacent angle. It is like finding the cotangent but backwards.

• Last but not least, the secant. You find the secant by dividing the hypotenuse by the adjacent angle.

Finding opposite and adjacent angles

• To find the opposite angle, one simple way to determine that is to find the opposite side to that angle you are trying to find. For instance, when finding an angle, one side is 200, the adjacent side is 500. We must divide the opposite angle by the adjacent angle to find the missing angle. 200/500 = 0.4, so the missing angle is 0.4.

• To find the adjacent angle, that is always the side right next to a given angle.

Hope this helps!