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Trigonometric Functions

### When using the half-angle formulas for trigonometric functions of $$alpha/2$$, I determine the sign based on the quadrant in which $$alpha$$ lies.Determine whether the statement makes sense or does not make sense, and explain your reasoning.

Trigonometric Functions

### $$\displaystyle{4}{{\cos}^{{2}}{x}}−{3}={0}$$

Trigonometric Functions

### Given the values for sin t and cos t, use reciprocal and quotient identities to find the values of the other trigonometric functions of t. $$\displaystyle{\sin{{t}}}=\frac{{3}}{{4}}{\quad\text{and}\quad}{\cos{{t}}}=\frac{\sqrt{{7}}}{{4}}$$

Trigonometric Functions

### Sketch a right triangle corresponding to the trigonometric function of the acute angle theta. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of theta. $$\displaystyle{\cos{\theta}}=\frac{{21}}{{5}}$$

Trigonometric Functions

### Use the figures to find the exact value of the trigonometric function $$\displaystyle{\tan{{2}}}\theta$$.

Trigonometric Functions

### Find the exact value of sin 60°.

Trigonometric Functions

### You see that the shadow of a nearby 6-foot tall street sign is 3 feet 6 inches. You measure the shadow of the rock wall to be 22 feet 3 inches. What method can you use with this information to approximate the height of the rock wall? Approximate the height of the rock wall.

Trigonometric Functions

### To further justify the Cofunction Theorem, use your calculator to find a value for the given pair of trigonometric functions. In each case, the trigonometric functions are cofunctions of one another, and the angles are complementary angles. Round your answers to four places past the decimal point. $$\displaystyle{{\sec{{6.7}}}^{\circ},}{\cos{{e}}}{c}{83.3}^{\circ}$$

Trigonometric Functions

### The two trigonometric functions defined for all real numbers are the_________ function and the_______ function. The domain of each of these functions is________ .

Trigonometric Functions

### The question asks for the exact value of the trigonometric function at the given real number: $$\displaystyle{\sin{{\left(\frac{{{3}\pi}}{{4}}\right)}}}$$

Trigonometric Functions

### Which statement cannot be true? Explain. A. $$\displaystyle{\sin{{A}}}={0.5}$$ B. $$\displaystyle{\sin{{A}}}={1.2654}$$ C. $$\displaystyle{\sin{{A}}}={0.9962}$$ D. PSKsin A = 3/4

Trigonometric Functions

### Let theta be an angle in standard position, $$\displaystyle{\sin{\theta}}{<}{0},{\cos{\theta}}{>}{0}$$. Name the quadrant in which theta lies.

Trigonometric Functions

### Given the following information about one trigonometric function, evaluate the other five functions. $$\displaystyle{\cos{{u}}}=\frac{{5}}{{13}}$$ , where $$\displaystyle{0}\le{u}\le\frac{\pi}{{2}}.$$

Trigonometric Functions

### Find the values of the other trigonometric functions of theta if $$\displaystyle{\cot{\theta}}=-\frac{{4}}{{3}}{\quad\text{and}\quad}{\sin{\theta}}{<}{0}$$.

Trigonometric Functions

### Find derivative of trigonometric function $$\displaystyle{y}=\frac{{{3}{\left({1}-{\sin{{x}}}\right)}}}{{{2}{\cos{{x}}}}}$$

Trigonometric Functions

### Find the derivative of $$y=\sin(\pi x)$$

Trigonometric Functions

### $$\displaystyle=\sqrt{{{3}{i}}}+\pi{j}+{c}{k},{v}={4}{i}−{j}−{k}$$, where is a constant. (a) Compute ‖u‖, ‖v‖, and u ∙ v for the given vector in R3. (b) Verify the Cauchy-Schwarz inequality for the given pair of vector.

Trigonometric Functions

### $$= \sqrt{3i} + \pi + ck, v = 4i − j−k$$, where is a constant. (a) Compute ‖u‖, ‖v‖, and u ∙ v for the given vector in R3. (b) Verify the Cauchy-Schwarz inequality for the given pair of vector.

Trigonometric Functions