Question

How do you find the value of \[\sin 270\]?

Answer 1

Hint: Real functions which relate any angle of a right-angled triangle to the ratio of any two of its sides are Trigonometric functions. We can also use geometric definitions to evaluate trigonometric values. Here, it’s important that we know the sine of theta is the ratio of the opposite side to the hypotenuse.

Complete step by step solution:
According to the given question, we need to evaluate \[\sin 270\].
If in a right angled triangle \[\theta \] represents one of its acute angle then by definition we can write
\[\sin \theta =\dfrac{Opposite}{Hypotenuse}\]
We know that sin 270 can be expressed as
\[sin\text{ }270=\text{ }sin\left( 3\times 90\text{ }+0\text{ } \right)\]
Also, we know that
\[sin\text{ }\left( 90{}^\circ \text{ }+\text{ }\theta \right)\text{ }=\text{ }cos\text{ }\theta \]
\[sin\left( 270 \right)=-cos0\]
Now as $\cos 0=1$,

Therefore sin(270)=−1.

Note:
One should be careful while evaluating trigonometric values and rearranging the terms to convert from one function to the other. Trigonometric functions are real functions that relate any angle of a right-angled triangle to the ratio of any two of its sides. The widely used ones are sin, cos, and tan.