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Triangle PQR, triangle RST and two angle measures are shown below
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Answer:
tan(θ) is undefined.
Step-by-step explanation:
Recall that tan(θ) = sin(θ) / cos(θ). We are given that sin(θ) = -1. Hence:
Since 1 / cos(θ) = sec(θ):
We can square both sides:
From the Pythagorean Identity:
Substitute:
So:
Since we acquire an untrue statement, no solutions exist.
If needed, refer to the unit circle. Recall that sin(θ) only equals -1 when θ = 3π/2 (on the interval [0, 2π)). At 3π/2, cos(θ) = 0. Since tan(θ) = sin(θ) / cos(θ), tan(θ) is undefined whenever sin(θ) = -1 (or 1).
Answer:
Slope = -⅓
Step-by-step explanation:
The equation for the slope of a straight line is
m = (y₂ - y₁)/(x₂ - x₁)
The line passes through (-1, 2) and (-4, 3).
m = (3 - 2)/[-4 - (-1)]
= 1/(-4 + 1)
= -⅓
The slope of the line is -⅓.
The Figure below shows the graph of your line through (-1, 2) and (-4, 3) with a slope of -⅓.
