Q: Write the following function in terms of its cofunction. Assume that all angles in which an unknown appears are acute angles. sin (θ + 25°) (Simplify your answer. Do not include the degree symbol in your answer.)

The correct answer is: $\cos(65-\theta)$ Explanation We use the cofunction identity $\sin x=\cos(90-x)$ for acute angles. Steps: Start with the identity: $$\sin(\theta+25)=\cos\bigl(90-(\theta+25)\bigr)$$ Simplify inside the cosine: $$\cos(90-\theta-25)$$ Combine constants: $$\cos(65-\theta)$$ Therefore, $\sin(\theta+25)=\cos(65-\theta)$.

Q: 17. How many years are in 84 months?

The correct answer is: $7\text{ years}$ Explanation To convert months to years, divide the number of months by 12 (months per year). Steps: Formula: $$\text{years}=\frac{\text{months}}{12}$$ Substitute: $$\text{years}=\frac{84}{12}$$ Compute: $$\text{years}=7$$ Therefore, 84 months equals $7\text{ years}$.

Q: 1. Write 4.3125 as a fraction in simplest form.

The correct answer is: $69/16$ Explanation We convert the decimal part to a fraction and simplify. Steps: Separate the integer and decimal parts: $$4.3125 = 4 + 0.3125$$ Write the decimal as a fraction: $$0.3125 = \frac{3125}{10000}$$ Simplify the fraction by dividing numerator and denominator by $125$: $$\frac{3125}{10000} = \frac{25}{80} = \frac{5}{16}$$ Combine and convert to an improper fraction: $$4 + \frac{5}{16} = \frac{64}{16} + \frac{5}{16} = \frac{69}{16}$$ Therefore, $4.3125 = \frac{69}{16}$.

Q: Write and solve an equation that represents the following: Twenty more than a number is eighteen.

The correct answer is: $x = -2$ Explanation Let $x$ be the unknown number. "Twenty more than a number is eighteen" translates to the equation $x + 20 = 18$. Solve this equation to find $x$. Steps: Write the equation: $x + 20 = 18$ Subtract 20 from both sides: $x = 18 - 20$ Compute the result: $x = -2$ Therefore, the number is $-2$.

Q: We want to convert 54 degrees Celsius (°C) to degrees Fahrenheit (°F).

The correct answer is: $129.2^\circ\text{F}$ Explanation Use the Celsius-to-Fahrenheit conversion formula $F = C\times\frac{9}{5}+32$. For $C=54^\circ\text{C}$ substitute and compute. Steps: Formula: $$F = C\times\frac{9}{5}+32$$ Substitute: $$F = 54\times\frac{9}{5}+32$$ Calculate: $$F = 54\times1.8+32 = 97.2+32 = 129.2$$ Therefore, $54^\circ\text{C} = 129.2^\circ\text{F}$.

Q: How do you write 0.79 as a fraction?

The correct answer is: $79/100$ Explanation Write the decimal as a fraction by moving the decimal point two places (because there are two digits after the decimal) — this is equivalent to multiplying numerator and denominator by 100. Steps: Multiply to remove the decimal: $$0.79\times100=79$$ Write as a fraction: $$0.79=\frac{79}{100}$$ Simplify if possible: $$\gcd(79,100)=1\text{, so the fraction is already in lowest terms}$$ Therefore, $0.79=\frac{79}{100}$.

Question

Write the following function in terms of its cofunction. Assume that all angles in which an unknown appears are acute angles. sin (θ + 25°) (Simplify your answer. Do not include the degree symbol in your answer.)

Accepted Answer

The correct answer is: $\cos(65-	heta)$

Explanation

We use the cofunction identity $\sin x=\cos(90-x)$ for acute angles.

Steps:

Start with the identity: $$\sin(	heta+25)=\cos\bigl(90-(	heta+25)\bigr)$$
Simplify inside the cosine: $$\cos(90-	heta-25)$$
Combine constants: $$\cos(65-	heta)$$

Therefore, $\sin(	heta+25)=\cos(65-	heta)$.