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Without using a calculator, decide whether the function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles.)

cos 2
Is the value of the function
cos 2 positive or negative?
positive
negative

Without using a calculator, decide whether the function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles.) $\newline$ $\cos 2$ $\newline$ Is the value of the function $\cos 2$ positive or negative? $\newline$ positive $\newline$ negative

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Coterminal and reference angles

Full solution

Q. Without using a calculator, decide whether the function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles.)

\newline

\cos 2

\newline

Is the value of the function

\cos 2

positive or negative?

\newline

positive

\newline

negative

Recognize interval for $2$ radians: Step $1$ : Recognize the interval for $2$ radians. $2$ radians is slightly more than $\pi$ (which is approximately $3.14$ ), so $2$ radians falls between $0$ and $\pi/2$ .
Determine sign of cosine function: Step $2$ : Determine the sign of the cosine function in this interval. The cosine function is positive in the first quadrant $0$ to $\pi/2$ .
Cosine of $2$ radians: Step $3$ : Since $2$ radians is in the first quadrant, the cosine of $2$ radians is positive.

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