Six-Trig Ratio│Please Help!

Question

Given the point (-3√2, -13) determine the six-trig ratio. Determine the two complementary angles. Label the angles L, M, N, with M being the right angle.

Answer 1

(3√2,-13) = (x,y)

X^2 + y^2 = r^2

(3√2)^2 + (-13)^2 = r^2

18+169

187 =r^2

√187 = r

Sin = y/r = -13/√187 = (13/√187)*(√187/√187)= -13√187/187

Cos =x/r= 3√2/ √187= (3√2/√187)*(√187/√187) = 3√374/187

Tan = y/x= -13/3√2= (-13/3√2)/(3√2/3√2)=-39√2/18

Csc=

Answer 2

Given Point

The given point is (-3√2, -13).

Calculating the Radius

The radius r is calculated using the formula:

r = √(x² + y²)

Substituting the values:

x = -3√2

y = -13

r = √((-3√2)² + (-13)²)

r = √(18 + 169) = √(187)

Trigonometric Ratios

1. Sine (sin):

  sin(L) = y/r = (-13)/√(187)

2. Cosine (cos):

  cos(L) = x/r = (-3√2)/√(187)

3. Tangent (tan):

  tan(L) = y/x = (-13)/(-3√2) = 13/(3√2)

4. Cosecant (csc):

  csc(L) = r/y = √(187)/(-13)

5. Secant (sec):

  sec(L) = r/x = √(187)/(-3√2)

6. Cotangent (cot):

  cot(L) = x/y = (-3√2)/(-13) = (3√2)/13

Complementary Angles

In a right triangle where M is the right angle, the angles L and N are complementary.

Let N be the angle complementary to L:

N = 90° - L

Summary of Trigonometric Ratios

sin(L) = (-13)/√(187)

cos(L) = (-3√2)/√(187)

tan(L) = 13/(3√2)

csc(L) = √(187)/(-13)

sec(L) = √(187)/(-3√2)

cot(L) = (3√2)/13

Angles

L is the angle formed by the radius with the positive x-axis.

M = 90° (right angle).

N = 90° - L (complementary to L).

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