Calculate cos, sin and tan of an angle - High school Trigonometry Exercises

Find the \cos\left(a\right) in the following triangle:

\cos\left(a\right)=\dfrac{3}{5}

\cos\left(a\right)=\dfrac{4}{5}

\cos\left(a\right)=\dfrac{3}{4}

\cos\left(a\right)=\dfrac{4}{3}

The cosine of an angle in a right triangle is equal to the quotient of the lengths of the adjacent side and the hypotenuse.

In this question:

The side adjacent to the angle a has a length of 3
The hypotenuse has a length of 5.

Therefore:

\cos \left(a\right) = \dfrac{3}{5}

Find the \cos\left(a\right) in the following triangle:

\cos\left(a\right)=\dfrac{1}{3}

\cos\left(a\right)=\dfrac{4}{\sqrt{2}}

\cos\left(a\right)=3

\cos\left(a\right)=8\sqrt{2}

The cosine of an angle in a right triangle is equal to the quotient of the lengths of the adjacent side and the hypotenuse.

In this question:

The side adjacent to the angle a has a length of 2
The hypotenuse has a length of 6.

Therefore:

\cos \left(a\right) = \dfrac{2}{6}= \dfrac{1}{3}

Find the \tan\left(a\right) in the following triangle:

\tan \left(a\right) = 0.6

\tan \left(a\right) = \dfrac{5}{3}

\tan \left(a\right) = \dfrac{\sqrt{34}}{15}

\tan \left(a\right) = \dfrac{\sqrt{34}}{3}

The tangent of an angle in a right triangle is equal to the quotient of the lengths of the opposite side and the adjacent side.

In this question:

The side opposite to the angle a has a length of 5.
The side adjacent to the angle a has a length of 3.

Therefore:

\tan \left(a\right) = \dfrac{5}{3}

Find the \sin \left(a\right) in the following triangle:

\sin \left(a\right) = \dfrac{5}{6}

\sin \left(a\right) = 1.5

\sin \left(a\right) = \dfrac{2}{3}

\sin \left(a\right) = 1.2

The sine of an angle in a right triangle is equal to the quotient of the lengths and the opposite side to the hypotenuse.

In this question:

The side opposite to the angle a has a length of 4.
The hypotenuse has a length of 6.

Therefore:

\sin \left(a\right) = \dfrac{4}{6}=\dfrac{2}{3}

Find the \tan \left(a\right) in the following triangle:

\tan \left(a\right) = \dfrac{1}{\sqrt{2}}

\tan \left(a\right) = \sqrt{2}

\tan \left(a\right) = 1

\tan \left(a\right) = 4\sqrt{2}

The tangent of an angle in a right triangle is equal to the quotient of the lengths of the opposite side and the adjacent side.

In this question:

The side opposite to the angle a has a length of 2.
The side adjacent to the angle a has a length of 2.

Therefore:

\tan \left(a\right) = \dfrac{2}{2}=1

Find the \sin \left(a\right) in the following triangle:

\sin \left(a\right) = \dfrac{7}{2\sqrt{6}}

\sin \left(a\right) = 14\sqrt{6}

\sin \left(a\right) = \dfrac{2\sqrt{6}}{7}

\sin \left(a\right) = \dfrac{7}{5}

The sine of an angle in a right triangle is equal to the quotient of the lengths of the opposite side and the hypotenuse.

In this question:

The side opposite to the angle a has a length of 2\sqrt{6}.
The hypotenuse has a length of 7.

Therefore:

\sin \left(a\right) = \dfrac{2\sqrt{6}}{7}.

Find the \cos\left(a\right) in the following triangle:

\cos \left(a\right) = \dfrac{2}{\sqrt{3}}

\cos\left(a\right)=\dfrac{1}{2}

\cos \left(a\right) = \sqrt{\dfrac{3}{6}}

\cos \left(a\right) = \dfrac{\sqrt{3}}{3}

The cosine of an angle in a right triangle is equal to the quotient of the lengths of the adjacent side and the hypotenuse.

In this question:

The side adjacent to the angle a has a length of \sqrt{3}.
The hypotenuse has a length of 3.

Therefore:

\cos \left(a\right) = \dfrac{\sqrt{3}}{3}