cos θ =
, sin θ =
, cot θ = 4/7, sec θ =
, cosec θ = 
<h3>What are trigonometric ratios?</h3>
Trigonometric Ratios are values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
Sin θ: Opposite Side to θ/Hypotenuse
Tan θ: Opposite Side/Adjacent Side & Sin θ/Cos
Cos θ: Adjacent Side to θ/Hypotenuse
Sec θ: Hypotenuse/Adjacent Side & 1/cos θ
Analysis:
tan θ = opposite/adjacent = 7/4
opposite = 7, adjacent = 4.
we now look for the hypotenuse of the right angled triangle
hypotenuse =
=
= 
sin θ = opposite/ hyp = 
Rationalize,
x
= 
But θ is in the third quadrant(180 - 270) and in the third quadrant only tan and cot are positive others are negative.
Therefore, sin θ = - 
cos θ = adj/hyp = 
By rationalizing and knowing that cos θ is negative, cos θ = -
cot θ = 1/tan θ = 1/7/4 = 4/7
sec θ = 1/cos θ = 1/
= -
cosec θ = 1/sin θ = 1/
= 
Learn more about trigonometric ratios: brainly.com/question/24349828
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Answer:
diagonal = = 12.8 inches (to the nearest tenth of an inch)
Step-by-step explanation:
As shown in the diagram attached to this solution:
Let the Length of the rectangular board = a
Let the width = b
Let the diagonal = d
where:
a = 10 inches
b = 8 inches
d = ?
Triangle ABC in the diagram is a right-angled triangle, therefore, applying Pythagoras theorem:
(hypotenuse)² = (Adjacent)² + (Opposite)²
d² = 10² + 8²
d² = 100 + 64
d² = 164
∴ d = √(164)
d = 12.806 inches
d = 12.8 inches (to the nearest tenth of an inch)
<em>N:B Rounding off to the nearest tenth of an inch is the same as rounding off to 1 decimal place.</em>
Answer:
C.

Step-by-step explanation:
