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Question

Find out the values of angle 270° for all the six trigonometric ratios.


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Solution

Step 1: Compute the sine and cosine of the given angle.

In the question, the measure of an angle 270° is given.

Compute the sine of the given angle.

We know that, sin180°+θ=-sinθ.

So,

sin(270°)=sin(180°+90°)sin(270°)=-sin(90°)sin(270°)=-1

Compute the cosine of the given angle.

We know that, cos180°+θ=-cosθ.

So,

cos(270°)=cos(180°+90°)cos(270°)=-cos(90°)cos(270°)=0

Step 2: Compute the tangent and cotangent of the given angle.

Compute the tangent of the given angle.

We know that, tan180°+θ=tanθ.

So,

tan(270°)=tan(180°+90°)tan(270°)=tan(90°)tan(270°)=N.DSince,tan(90°)=N.D

Compute the cotangent of the given angle.

We know that, cot180°+θ=cotθ.

So,

cot(270°)=cot(180°+90°)cot(270°)=cot(90°)cot(270°)=0

Step 3: Compute the secant and cosecant of the given angle.

Compute the secant of the given angle.

We know that, sec180°+θ=-secθ.

So,

sec(270°)=sec(180°+90°)sec(270°)=-sec(90°)sec(270°)=N.Dsince,sec(90°)=N.D

Compute the cosecant of the given angle.

We know that, cosec180°+θ=-cosecθ.

So,

cosec(270°)=cosec(180°+90°)cosec(270°)=-cosec(90°)cosec(270°)=-1

Hence, the values of trigonometric ratios are

sin270=-1cos270=0tan270=Undefinedcosec270=-1sec270=Undefinedcot270=0


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