which one of the following functions is equivalent to cos 260deg?

Question

a. cos 80deg
b. cos 10 deg
c. -cos 10deg
d. -cos 80deg

Answer 1

d.
because 260 degrees is 80 degrees past 180, and in the third quadrent, where cos is always negative.
80 degrees in the 1st quadrent would be positive, but
the answer 'd' has a negative sign, making it the same value as cos 280 degrees.

Answer 2

Think about it in terms of quadrants (the four parts of a Cartesian coordinate system). Cosine is positive for the two right quadrants (termed I and IV), while it's negative for the left quadrants (II and III).
Next, think about where 260deg is: it's just to the left of the negative y-axis. Cosine is negative there.
As for the answers, both a and b are in the positive cosine section, so they're wrong.
Think about the others in terms of location. 10deg is close to the x-axis - but 260deg is close the y axis. 80deg is also close the y-axis. Since cosine is positive in this quadrant, taking the negative of it gives you the correct answer.
You should also realize that cos (x) = -cos (x-180)
260 - 180 = 80
Thus, if x = 260, cose (260) = -cos (260-180) = -cos (80)

Answer 3

Again, use your reference angle and the quadrant
mnemonic ASTC.
The reference angle for 260 degrees is 80
degrees and we are in quadrant III, so
the answer is d. - cos 80 degrees.

Answer 4

f(x)=cos(x)and g(x)=x^3+1. Find: d/dx g(f(x))= g( f(x))=(f(x)^3)+1. = (cos x)^3+1= cos^3 x+1 g( f(x))=cos^3 x+1 d/ dx g( f(x))=d /dx (cos^3 x+1)=d /dx cos^3 x+d /dx1= 3 cos ^2 x d/dx (cos x)+0= 3 cos^2 x(-sin x) =-3sin x cos^2 x

Answer 5

-cos 80 (d)