Answer:
Given point (5,-12) falls into IV quadrant
<u>The right triangle with legs of 5 and -12, and hypotenuse is:</u>
- √5² + (-12)² = √25+144 = √169 = 13
<u>Value of sinθ, cosθ, and tanθ:</u>
- sin θ = -12/13
- cos θ = 5/13
- tan θ = -12/5
You buy 3 books that each cost the same amount and a magazine all for 55.99. You know that the magazine costs 1.99. How much doe
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Answer:
90°
Step-by-step explanation:
The angle between the vectors can be found any of several ways. Here, we observe that the segments from the origin to the two points are at right angles to each other. (Their slopes are opposite reciprocals.) Hence the angle between the vectors is 90°.
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The slope to point 'a' is y/x = 2/1 = 2.
The slope to point 'b' is y/x = (-1/2)/1 = -1/2.
The product of these slopes is (2)(-1/2) = -1, indicating the vectors are perpendicular. The angle between them is 90°.
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We can also use the trig formula for the tangent of the difference of angles.
tan(α-β) = (tan(α) -tan(β))/(1 +tan(α)tan(β))
The tangents are the slopes, calculated above, so we have ...
tan(α -β) = (2 -(-1/2))/(1 +(2)(-1/2)) = (5/2)/0 = <em>undefined</em>
The tangent is <em>undefined</em> for angles that are odd multiples of 90°. The angle between the vectors is 90°.
