Defining Sine and Cosine in Trigonometry

5.3 Definition of sine, cosine, & tangent

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Students

Take

Calculus

Multiple Choice

If angle $$\theta$$ is in the 1st quadrant, is $$\cos\theta$$ positive or negative?

• Positive

• Negative

• could be both positive or negative

• I don't know

Multiple Choice

If angle $$\theta$$ is in the 2nd quadrant, is $$\sin\theta$$ positive or negative?

• Positive

• Negative

• could be both positive or negative

• I don't know

Multiple Choice

If angle $$\theta$$ is in the 3rd quadrant, is $$\cos\theta$$ positive or negative?

• Positive

• Negative

• could be both positive or negative

• I don't know

Multiple Choice

If angle $$\theta$$ is in the 4th quadrant, is $$\tan\theta$$ positive or negative?

• Positive

• Negative

• could be both positive or negative

• I don't know

Locate section #2.

​Sketch a picture of each angle. State whether each trig function is positive or negative.

​Go to 4.10 Practice

​Sketch the angle

Multiple Choice

Given $$\sin-240\degree$$ , in which quadrant is this angle located?

• 1st quardrant

• 2nd quadrant

• 3rd quadrant

• 4th quadrant

Multiple Choice

Given $$\sin-240\degree$$ , is this trig value positive or negative?

• Positive

• Negative

• Could be both positive or negative

• I don't know

Multiple Choice

Given $$\cos\frac{2\pi}{3}$$ , in which quadrant is this angle located?

• 1st quardrant

• 2nd quadrant

• 3rd quadrant

• 4th quadrant

Multiple Choice

Given $$\cos\left(\frac{2\pi}{3}\right)$$ , is this trig value positive or negative?

• Positive

• Negative

• Could be both positive or negative

• I don't know

Multiple Choice

Given $$\tan\frac{\pi}{4}$$ , in which quadrant is this angle located?

• 1st quardrant

• 2nd quadrant

• 3rd quadrant

• 4th quadrant

Multiple Choice

Given $$\tan\frac{\pi}{4}$$ , is this trig value positive or negative?

• Positive

• Negative

• Could be both positive or negative

• I don't know

​Complete d, e, f independently

Find values for sin, cos, tan given a point P (x, y).

​Next section

#3

​Use this part of notes on the front page

Multiple Choice

Which quadrant is P(6,-8) located?

• 1st quadrant

• 2nd quadrant

• 3rd quadrant

• 4th quadrant

Multiple Choice

Given the point P(6, -8), which equation should be used to find the hypotenuse?

• $$\sqrt{\ 6+\left(-8\right)}$$

• $$\sqrt{\ 6\cdot\left(-8\right)}$$

• $$36+64$$

• $$\sqrt{\ 36+64}$$

Multiple Choice

Given the point P(6, -8), what is the length of hypotenuse?

• $$\sqrt{\ 14}$$

• $$100$$

• $$10$$

• $$\sqrt{\ 48}$$

Multiple Choice

Given the point P(6, -8), is $$\sin\theta$$ positive or negative?

• Positive

• Negative

Multiple Choice

Given the point (6, -8), what is the value of $$\sin\theta$$ ?

(Hint: you should ALWAYS simplify the fraction to the lowest term)

• $$\frac{3}{5}$$

• $$-\frac{4}{5}$$

• $$-\frac{8}{10}$$

• $$-\frac{4}{3}$$

Multiple Choice

Given the point P(6, -8), is $$\cos\theta$$ positive or negative?

• Positive

• Negative

Multiple Choice

Given the point (6, -8), what is the value of $$\cos\theta$$ ?

(Hint: you should ALWAYS simplify the fraction to the lowest term)

• $$\frac{3}{5}$$

• $$-\frac{4}{5}$$

• $$\frac{6}{10}$$

• $$-\frac{4}{3}$$

Multiple Choice

Given the point P(6, -8), is $$\tan\theta$$ positive or negative?

• Positive

• Negative

Multiple Choice

Given the point (6, -8), what is the value of $$\tan\theta$$ ?

(Hint: you should ALWAYS simplify the fraction to the lowest term)

• $$\frac{3}{5}$$

• $$-\frac{4}{5}$$

• $$-\frac{8}{6}$$

• $$-\frac{4}{3}$$

locate the point, connect the point with origin, & sketch the angle

Multiple Choice

Which quadrant is P(3, 4) located?

• 1st quadrant

• 2nd quadrant

• 3rd quadrant

• 4th quadrant

Multiple Choice

Given the point P(3, 4), which equation should be used to find the hypotenuse?

• $$\sqrt{\ 3+4}$$

• $$\sqrt{\ 3\cdot4}$$

• $$9+16$$

• $$\sqrt{\ 9+16}$$

Multiple Choice

Given the point P(3, 4), what is the length of hypotenuse?

• $$\sqrt{\ 7}$$

• $$25$$

• $$5$$

• $$\sqrt{\ 12}$$

Multiple Choice

Given the point P(3, 4), is $$\sin\theta$$ positive or negative?

• Positive

• Negative

Multiple Choice

Given the point (3, 4), what is the value of $$\sin\theta$$ ?

• $$\frac{3}{5}$$

• $$\frac{4}{5}$$

• $$\frac{5}{4}$$

• $$-\frac{4}{3}$$

Multiple Choice

Given the point P(3, 4), is $$\cos\theta$$ positive or negative?

• Positive

• Negative

Multiple Choice

Given the point (3, 4), what is the value of $$\cos\theta$$ ?

• $$\frac{3}{5}$$

• $$\frac{4}{5}$$

• $$-\frac{3}{4}$$

• $$\frac{4}{3}$$

Multiple Choice

Given the point P(3, 4), is $$\tan\theta$$ positive or negative?

• Positive

• Negative

Multiple Choice

Given the point (3, 4), what is the value of $$\tan\theta$$ ?

• $$\frac{3}{5}$$

• $$\frac{4}{5}$$

• $$\frac{3}{4}$$

• $$\frac{4}{3}$$

Poll

How well do you know about finding sin, cos, tan given a point?

• I am confident with this

• I understand most of it

• I understand some of it

• I need a lot of help with this