Daily Challenge 1: Odd-and-Even and Cofunction Identities

$$f\left(-x\right)=f\left(x\right)$$

even function

$$f\left(-x\right)=-f\left(x\right)$$

odd function

neither odd nor even function

$$f\left(-x\right)=f\left(x\right)$$

even function

$$f\left(-x\right)=-f\left(x\right)$$

odd function

neither odd nor even function

$$f\left(-x\right)=f\left(x\right)$$

even function

$$f\left(-x\right)=-f\left(x\right)$$

odd function

neither odd nor even function

red and blue

green and blue

red and green

symmetric with respect to the x-axis

symmetric with respect to the y-axis

symmetric with respect to the origin

not symmetric

symmetric with respect to the x-axis

symmetric with respect to the y-axis

symmetric with respect to the origin

not symmetric

$$\frac{\pi}{2}$$ to the right

$$\frac{\pi}{2}$$ to the left

$$\pi$$ to the right

$$\pi$$ to the left

$$\sin x=\cos\left(x+\frac{\pi}{2}\right)$$

$$\sin x=\cos\left(x-\frac{\pi}{2}\right)$$

$$\sin x=\cos\left(x+\pi\right)$$

$$\sin x=\cos\left(x-\pi\right)$$

sine is an odd function

sine is an even function

cosine is an odd function

cosine is an even function

$$\sin\left(\frac{\pi}{2}-x\right)=\cos x$$

$$\cos\left(\frac{\pi}{2}-x\right)=\sin x$$

$$\sin\left(\frac{\pi}{2}+x\right)=\cos x$$

$$\cos\left(\frac{\pi}{2}+x\right)=\sin x$$