Answer: Because
, therefore
.
Step-by-step explanation:
1. All the trigonometric values can be found using the unit circle. See attached table.
2. Graph:
desmos.com/calculator/10n7yrm3tm
3. All trig functions are periodic functions. The period of secant and cosecant is 2π. The period of cotangent is π.
4. Using the table from step 1 and the graph from step 2, secant has a domain of x ≠ pi/2, 3pi/2 and a range of x ≤ -1, x ≥ 1. Cotangent has a domain of x ≠ 0, pi, 2pi and a range of -∞ < x < ∞.
5. Graph:
desmos.com/calculator/tldiqt7qra
Cosecant has the same graph as secant shifted π/2 to the right. So they have different domains, but the same range.
Answer: the slope is -1/5
Example:
Answer: She is correct that she can use a division expression.
It would be $4/(2/3) OR 4 ÷ 2/3 = cost per pound.
Not an easy division, but using the rule: invert the divisor and multiply.
4 × 3/2 = 6 So the cost is $6 per pound.
Step-by-step explanation: It would be easier to answer if the statements were included.
Using a decimal equivalent for 2/3, 4/0.667 is an easy division expression to solve on a calculator.