Write the following expression as a function of a positive acute angle. sec280°

Answers

sin (312°) = - sin (48°)

Justification:

1) 312° ⇒ 270° < 312° < 360° ⇒ third quadrant ⇒ sign of sin (312°) is negative

2) Acute angle:

angle = 360° - 312° = 48°

⇒ sin (312°) = - sin (48°) ← this is the expression requested.

Using the calculator you can find the value sin (312°) = - sin (48°) ≈ - 0.743

Since the trigonometric functions are periodic, we know that

\cos(x)=\cos(x+360)

In this case, you have

\cos(-240)=\cos(-240+360)=\cos(120)

Finally, we have

\cos(120)=\cos(90+30)

and you can use the formula

\cos(90+x)=-\sin(x)

To conclude

\cos(120)=\cos(90+30)=-\sin(30)

cos(-240°) = cos 120°; the "adjacent sides" and the "hypotenuses" are the same in both cases.  The supplement of 120° is 60°, and 60° is a positive acute angle.  Since cos(-240°) is negative, we need to write

cos(-240°) = -cos(60°).  

Check:  cos(60°)= 1/2, so - cos(60°) = -1/2, which is the value of cos(-240°).

As property of trigonometric cosine function, we have:

cos(x) = cos(-x)

=> cos(-240) = cos(240)

Otherwise, we also have:

cos(x + 180) = -cos(x)

=> cos(240) = - cos(60)

=> cos(-240) = cos(+240) = -cos(+60)

Hope this helps!

:)

205

Step-by-step explanation:

- cos 35°

Step-by-step explanation:

215° is in the third quadrant where cos is negative

cos 215° = - cos( 215 - 180)° = - cos 35°



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