use a trigonometric identity to find the indicated value in the specified quadrant. Function Value sin θ = - 3/5 Quadrant IV Value cos θ

If θ is an acute angle of a right triangle and sin θ = 3/5, what is the value of cos θ?

find the values of the six trigonometric functions of θ with the given constraint. Function Value sec θ = -2 Constraint sin θ < 0

Determine whether the vectors lie in a plane, and if so, whether they lie on a line. (a) $\mathbf{v}_{1}=(1,2,1), \mathbf{v}_{2}=(-7,1,3), \mathbf{v}_{3}=(-14,-1,-4)$ (b) $\mathbf{v}_{1}=(2,1,-1), \mathbf{v}_{2}=(1,3,4), \mathbf{v}_{3}=(1,1,0)$ (c) $\mathbf{v}_{1}=(6,-4,8), \mathbf{v}_{2}=(-3,2,-4), \mathbf{v}_{3}=(9,-6,-12)$.

A basket manufacturer has headquarters in an office building that has the same shape as a basket they sell. The bottom of the basket is a rectangle with length 15 inches and width 10 inches. The base of the building is a rectangle with length 192 feet. What is the width of the base of the building.

Find the exact value.

$$\sin \left(70^{\circ}\right) \cos \left(25^{\circ}\right)-\cos \left(70^{\circ}\right) \sin \left(25^{\circ}\right)$$

Write the sum as a product. sin 5x + sin 3x

Evaluate the expression. 24. 12(6) + 1/4 • 2²

Write the product as a sum. cos 5x cos 3x

A student wrote the following conjecture. Find a counterexample and explain the error. If x is a positive even number and y is any integer, then the product xy will be positive.

The amino acid sequence in one section of a protein is shown here. It represents which kind of structure? (primary, secondary, tertiary, or quaternary) -Lys-Glu-Thr-Ala -Ala-Ala-Lys-Phe-Glu-

Eliminate the parameter to find a Cartesian equation of the curve. y=(t+1)^1/2, y=(t-1)^1/2

A portfolio’s expected return is 12%, its standard deviation is 20%, and the risk-free rate is 4%. Which of the following would make for the greatest increase in the portfolio’s Sharpe ratio? a. An increase of 1% in expected return. b. A decrease of 1% in the risk-free rate. c. A decrease of 1% in its standard deviation.

A sequence is defined recursively.Write down the first five terms. $a_{1}=1 ;\ a_{n}=n-a_{n-1}$