Use the given values to evaluate (if possible) all six trigonometric functions. cotϕ=-3, sinϕ=

step 1 If we know that the cotangent is negative 3 and the sign is the square of 10 over 10, we want to

Use the given values to evaluate (if possible) all six...

Key Concepts

Quadrant Considerations

This concept involves using sign analysis to determine the correct signs of trigonometric functions based on the quadrant in which the angle lies. Knowing which functions are positive or negative in each quadrant is essential, especially when non?acute angle values are involved, to accurately evaluate all six trigonometric functions.

Pythagorean Identities

The Pythagorean identities, such as sin²? + cos²? = 1, provide a relationship between the sine and cosine functions. These identities are foundational in finding a missing trigonometric function when one is provided, thereby ensuring all computations maintain the inherent relationships of the trigonometric ratios.

Reciprocal Identities

Reciprocal identities relate pairs of trigonometric functions where one is the reciprocal of the other (e.g., secant is the reciprocal of cosine, and cosecant is the reciprocal of sine). Such identities are crucial when given one function’s value and needing to compute another function from it.

Trigonometric Function Definitions

This concept involves understanding the fundamental definitions of trigonometric ratios such as sine, cosine, tangent, cotangent, secant, and cosecant, typically in relation to the sides of a right triangle or via the unit circle. These definitions allow one to express some functions in terms of others, for instance, cotangent being the ratio of cosine to sine.

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