Question

5. Given sec theta = 13/12 calculate all other trigonometric ratios.
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Answer 1

It is given that secθ=13/12.

The formula for cosine function is,

cosθ=1/secθ

cosθ=1/ (13/12)

cosθ=12/13

Draw triangle ABC according to given conditions.(see attachment)

The formula for cosine function is,

cosθ=AB/AC

AB/AC=12/13

Let, the value of AC=13x and AB=12x.

Use Pythagoras theorem in given triangle ABC as,

AC^2=AB^2+BC^2

Substitute the values of AC=13x and AB=12x in the above formula we get.

(13x)^2=(12x)^2+(BC)^2

169x^2=144x^2+(BC)^2

(BC)^2=25x^2

BC=5x

The formula for sine function is,

sinθ=BC/AC

Substitute the values BC=5x and AC=13x in the above formula we get,

sinθ=5x/13x

sinθ=5/13

The formula for cosecant function is,

cosecθ=1/sinθ

cosecθ=13/5

The formula for cosine function is,

cosθ=AB/AC

Substitute the values AC=13x and AB=12x in the above formula we get,

cosθ=12/13

The formula for tangent function is,

tanθ=BC/AB

Substitute the values BC=5x and AB=12x in the above formula we get,

tanθ=5x/12x

tanθ=5/12

The formula for cotangent function is,

tanθ=1/cotθ

cotθ=12/5

Thus, the values are cotθ=12/5, tanθ=5/12, sinθ=5/13, cosecθ=13/5 and cosθ=12/13.

Answer 2

Answer:

see the picture okay.......................................