Till now you might have found that trigonometric identities are somehow inter-related. For example, if you check \sin and \cos graphs, they are related to each other. Another example is at { 45 }^{ \circ }, both \sin and \cos have the same values, does that mean that at every angle, they have some kind of relation? The answer is yes! And that is why this lesson focuses on cofunction identities.

Let's say, your teacher asked you to find the value of \cos when \sin is at angle { 60 }^{ \circ }, if you know cofunction trigonometric identities then this will be a piece of cake for you. Before we list the cofunction identities, you should know that two angles are complementary if the sum is { 90 }^{ \circ } or \frac { \pi }{ 2 } radians.

\sin { (\frac { \pi }{ 2 } - \alpha ) } = \cos { \alpha }

\cos { (\frac { \pi }{ 2 } - \alpha ) } = \sin { \alpha }

\tan { (\frac { \pi }{ 2 } - \alpha ) } = \cot { \alpha }

Let's come back to our case, so you need to find the value of \cos when when \sin is at angle { 60 }^{ \circ }. Now you know that \cos { (\frac { \pi }{ 2 } - \alpha ) } = \sin { \alpha } hence:

\sin { { 60 }^{ \circ } } = \sin { ({ 90 }^{ \circ } - { 60 }^{ \circ }) } = \cos { { 30 }^{ \circ } } = \frac { \sqrt { 3 } }{ 2 }

This is possible with other trigonometric ratios as well, for example:

\cos { { 60 }^{ \circ } } = \cos { ({ 90 }^{ \circ } - { 60 }^{ \circ }) } = \sin { { 30 }^{ \circ } } = \frac { 1 }{ 2 }

\tan { { 60 }^{ \circ } } = \tan { ({ 90 }^{ \circ } - { 60 }^{ \circ }) } = \cot { { 30 }^{ \circ } } = \sqrt { 3 }

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Hamza

Hi! I am Hamza and I am from Pakistan. My hobbies are reading, writing and playing chess. Currently, I am a student enrolled in the Chemical Engineering Bachelor program.