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 for sine and cosine (angles in degrees):$\sin x=\cos(90-x)$. Steps: Let $x=\theta+25$. Apply the identity: $$\sin(\theta+25)=\cos(90-(\theta+25))$$ Simplify inside the cosine: $$\cos(90-(\theta+25))=\cos(90-\theta-25)=\cos(65-\theta)$$ Therefore $\sin(\theta+25)=\cos(65-\theta)$. (As a check, using the evenness of cosine one may also write $\cos(65-\theta)=\cos(\theta-65)$, so both forms are equivalent.) Summary: By the cofunction identity $\sin x=\cos(90-x)$ and direct substitution $x=\theta+25$, the expression simplifies to $\cos(65-\theta)$ (degrees implied; the final answer omits the degree symbol as requested).

Q: The matrix below represents a system of equations.

Please provide the matrix so I help you analyze solve the system of equations it represents.

Q: Identify the scale factor used to graph the image below.

I need more information or the itself determine scale factor. Could you please upload the image or provide the measurements of the figure and its image?

Q: At which angle will the hexagon rotate so that it maps onto itself?

hexagon will onto at an angle of 60°. Explanation A hexagon has rotational symmetry of order6, meaning it maps onto itself after rotations of multiples $60°$ (since $360°/6 60°$). These rotations include $60° $120°$, $° $°$, $300°$, and $0°$ (a full rotation: Recognize that a regularagon has identical sides and. The symmetry rotations are spaced around the circle, dividing $360°$ into 6 parts. Therefore, the smallest non-zero angle for which the hexagon maps onto itself is $60°$. Hence, the hexagon will map itself when rotated by 60°$.

Q: The graph shows the four quadrants of the coordinate plane.An XY coordinate plane divided into four quadrants. The x axis runs from left to right. The y axis runs up and down. Quadrant 1 is the top right quadrant. Quadrant 2 is the top left quadrant. Quadrant 3 is the bottom left quadrant. Quadrant 4 is the bottom right quadrant. y x Quadrant I Quadrant II Quadrant III Quadrant IV Where is (−2.5,2) located on the coordinate plane?Choose 1 answer:Choose 1 answer:(Choice A) Quadrant I AQuadrant I (Choice B) Quadrant II BQuadrant II (Choice C) Quadrant III CQuadrant III (Choice D) Quadrant IV DQuadrant IV (Choice E) x -axisE x -axis(Choice F) y -axisF y -axis18 of 22

The correct answer is: Choice B Quadr II. **Explanation point $(-2.5, 2)$ has a negative x-coordinate and a positive y-coordinate. In the coordinate plane, Quadrant II contains points where the x-value is negative and the y-value is positive. Therefore, $(-2., 2)$ located in Quadrant II. Steps: The x-coordinate $-2.5$, is less than zero, the point is to the left of y-axis. The-coordinate is $2\ which is greater than zero, indicating the point is above the x. 3. Combining, the point is in the top-left section of the plane, which isant II. Hence, the point \((-2., 2)$ is in Quadrant II.

Q: What is the value of x?

I need information or the specific equation to determine value of $$. Please provide the complete problem or.

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 for sine and cosine (angles in degrees):$\sin x=\cos(90-x)$.

Steps:

Let $x=	heta+25$. Apply the identity:

$$\sin(	heta+25)=\cos(90-(	heta+25))$$

Simplify inside the cosine:

$$\cos(90-(	heta+25))=\cos(90-	heta-25)=\cos(65-	heta)$$

Therefore $\sin(	heta+25)=\cos(65-	heta)$. (As a check, using the evenness of cosine one may also write $\cos(65-	heta)=\cos(	heta-65)$, so both forms are equivalent.)

Summary: By the cofunction identity $\sin x=\cos(90-x)$ and direct substitution $x=	heta+25$, the expression simplifies to $\cos(65-	heta)$ (degrees implied; the final answer omits the degree symbol as requested).