Given vector u, what is the magnitude, |u|, and directional angle, θ, in standard position?
2 answers:
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Answer:
Tan E = 2 / 7.75
Sin G = 7.75 / 8
Sec G = 4
Step-by-step explanation:
Find the attached document for better illustration of the triangle
Assuming the hypothenus of the triangle is 8 = EG since it's the longest side of the triangle.
FG = 2 = opposite side of the triangle.
We can use pythagorean theorem to find the adjacent of the triangle since we already know two sides.
EG² = FG² + EF²
EF² = EG² - FG²
EF² = 8² - 2²
EF² = 64 - 4
EF² = 60
EF = √(60)
EF = 7.7459 = 7.75
To find the respective trignometric ratio, we can use the relation SOH CAH TOA
Sine = opposite / hypothenus
Cosine = adjacent/ hypothenus
Tangent = opposite/ adjacent
A. tan E
Tan E = opposite/ adjacent
Tan E = 2 / 7.75
Tan E = 0.2580
B. Sin G = opposite / hypothenus
Sin G = 7.75 / 8
Sin G = 0.9687
C. Sec G = 1 / cos G
Cos G = adjacent / hypothenus
Sec G = 1 / (adjacent / hypothenus)
Sec G = hypothenus/ adjacent
Sec G = 8 / 2
Sec G = 4
