Write the value of 10^ + 20^ + 30^ +...+ 360^ . - Vidyadip

Question

Write the value of $\sin10^\circ+\sin20^\circ+\sin30^\circ+...+\sin360^\circ.$

✓

Answer

$\sin(360^\circ-\theta)=-\sin\theta$ $\sin10^\circ+\sin20^\circ+...+\sin360^\circ$ $=\sin(360^\circ=350^\circ)+\sin(360^\circ-340^\circ)+\ ...\ \\\ +\sin180^\circ+\sin190^\circ+\ ...\ +\sin360^\circ$ $=-\sin350^\circ-\sin340^\circ-\ ...\ =\sin190^\circ\\\ \ \ \ +\sin180^\circ+\sin190^\circ+\ ...\ +\sin360^\circ$ $=\sin180^\circ+\sin360^\circ$ $=0+0$ $=0$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 1 marks)" from Trigonometric Functions→Trigonometric Functions — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Write down the all possible proper subset of the given set. {1, 2, 3}

If $a \neq b \neq c$, write the condition for which the equations $(b-c) x+(c-a) y+(a-b)=0$ and $\left(b^3-c^3\right) x+\left(c^3-a^3\right) y+$ $\left(a^3-b^3\right)=0$ represent the same line.

Two dice are thrown. The events A, B, and C are as follows:
A: getting an even number on the first die.
B: getting an odd number on the first die.
C: getting the sum of the numbers on the dice $\le$ 5.
state true or false: A and B are mutually exclusive and exhaustive (give the reason for your answer).

The given collections are sets or not? Justify your answer: The collection of all girls in your class.

For the following statements, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer. To apply for a driving licence, you should have a ration card or a passport.

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow\frac{1}{4}}\frac{4\text{x}-1}{2\sqrt{\text{x}}-1}$

A group consist of 4 girls and 7 boys. In how many ways, a team of 5 members be selected, if the team has no girl?

Write the setin the set-builder form:{2, 4, 6, . . . }

The given following sets are finite & in which of it infinite in if?
Set of letters of the English Alphabets;

List all the element of the following sets:
F = {x : x is a letter of the word "MISSISSIPPI"};