Problem 72
Question
Determine whether each statement makes sense or does not make sense, and explain your reasoning. The sine and cosine are cofunctions and reciprocals of each other.
Step-by-Step Solution
Verified Answer
The statement 'The sine and cosine are cofunctions and reciprocals of each other.' only makes partial sense. They are cofunctions of each other, but they are not reciprocals of each other.
1Step 1: Understand trigonometric functions
In trigonometry, sine and cosine are fundamental functions. They are not reciprocals of each other. Reciprocal of sine is cosecant, and reciprocal of cosine is secant. Therefore, the part of the statement saying they are reciprocals is incorrect.
2Step 2: Analyze cofunctions
The term 'cofunction' in trigonometry refers to functions where for all acute angles, their function values add up to 90 degrees. Sine and Cosine are indeed cofunctions because sin(x) = cos(90° - x), they satisfy the cofunction identity. Therefore, the part of the statement saying they are cofunctions is correct.
Other exercises in this chapter
Problem 71
Model motion in which the amplitude decreases with time due to friction or other resistive forces. Graph each function in the given viewing rectangle. How many
View solution Problem 72
Graph \(f, g,\) and \(h\) in the same rectangular coordinate system for \(0 \leq x \leq 2 \pi .\) Obtain the graph of h by adding or subtracting the correspondi
View solution Problem 72
Find the length of the arc on a circle of radius \(r\) intercepted by a central angle \(\boldsymbol{\theta}\). Express arc length in terms of \(\pi .\) Then rou
View solution Problem 72
In Exercises \(61-86,\) use reference angles to find the exact value of each expression. Do not use a calculator. $$\tan \frac{9 \pi}{2}$$
View solution