Angle (argument of a function): \(\alpha\)

Trigonometric functions: \(\sin \alpha,\) \(\cos \alpha,\) \(\tan \alpha,\) \(\cot \alpha\)

- Expressing the sine in terms of cosine

\(\sin \alpha = \pm \sqrt {1 – {{\cos }^2}\alpha } \)

Note: The sign in front of the radical on the right side depends on the quadrant in which the angle lies. The sign and value of a trigonometric function on the left side must coincide with the sign and value in the right side. This rule also applies to other formulas given below. - Expressing the sine in terms of tangent

\(\sin \alpha = \large\frac{{\tan \alpha }}{{ \pm \sqrt {1 + {{\tan }^2}\alpha } }}\normalsize\) - Expressing the sine in terms of cotangent

\(\sin \alpha = \large\frac{1}{{ \pm \sqrt {1 + {{\cot }^2}\alpha } }}\normalsize\) - Expressing the cosine in terms of sine

\(\cos \alpha = \pm \sqrt {1 – {{\sin }^2}\alpha } \) - Expressing the cosine in terms of tangent

\(\cos \alpha = \large\frac{1}{{ \pm \sqrt {1 + {{\tan }^2}\alpha } }}\normalsize\) - Expressing the cosine in terms of cotangent

\(\cos \alpha = \large\frac{{\cot \alpha }}{{ \pm \sqrt {1 + {{\cot }^2}\alpha } }}\normalsize\) - Expressing the tangent in terms of sine

\(\tan \alpha = \large\frac{{\sin \alpha }}{{ \pm \sqrt {1 – {{\sin }^2}\alpha } }}\normalsize\) - Expressing the tangent in terms of cosine

\(\tan \alpha = \large\frac{{ \pm \sqrt {1 – {{\cos }^2}\alpha } }}{{\cos \alpha }}\normalsize\) - Expressing the tangent in terms of cotangent

\(\tan \alpha = \large\frac{1}{{\cot \alpha }}\normalsize\) - Expressing the cotangent in terms of sine

\(\cot \alpha = \large\frac{{ \pm \sqrt {1 – {{\sin }^2}\alpha } }}{{\sin \alpha }}\normalsize\) - Expressing the cotangent in terms of cosine

\(\cot \alpha = \large\frac{{\cos \alpha }}{{ \pm \sqrt {1 – {{\cos }^2}\alpha } }}\normalsize\) - Expressing the cotangent in terms of tangent

\(\cot \alpha = \large\frac{1}{{\tan \alpha }}\normalsize\)