Question

20.
sin? 630 +sin_27°
+2sin36º. sin420. sec480. sec540 = ?
sec2200 + cot2700
O a) 5
en
O b) 3
O c) 10
O
d) 0​

Answer 1

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Answer 2

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Questions & Answers

CBSE

Mathematics

Grade 11

Trigonometry

Question

Answers

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How do you find the value of sin630

?

Answer

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Hint: We will write the value of the given angle by breaking it in terms of π

. Use the concept of complementary angles to write the value of sine of the angle by converting it into cosine of angle. Use the graph of cosine to calculate the value of the cosine at that angle.

* Two angles are said to be complementary to each other if the sum of angles is 90∘

. Sine and cosine are complementary angles, we write cosx=sin(90∘−x)

Complete step-by-step answer:

We have to find the value of sin630∘

We can write 630∘=4×180∘−90∘

Substitute the value of angle in the bracket of sine.

Then sin630∘=sin(4×180∘−90∘)

i.e. substitute the value of 180∘=π

and 90∘=π2

in the equation

⇒sin630∘=sin(4×π−π2)

Multiply the values in the bracket

⇒sin630∘=sin(4π−π2)

Take negative sign outside the angle and write the angle inside according to it

⇒sin630∘=sin(−(π2−4π))

Since sine is an odd function we can write sin(−θ)=−sinθ

, write the value of angle accordingly.

⇒sin630∘=−sin(π2−4π)

Now we know that sine and cosine are complementary angles, we write cosx=sin(90∘−x)

Then we can write sin(π2−4π)=cos4π

⇒sin630∘=−cos4π

… (1)

Now we draw the graph of cosine at angles from 0 to 4π

Here we see that cos4π=1

Substitute the value in equation (1)

⇒sin630∘=−1

∴

The value of sin630∘

is -1.