The following dot plot shows the number of chocolate chips in each cookie that Shawn has. Each dot represents a different cookie
.
2 answers:
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cos θ = , sin θ =
, cot θ = 4/7, sec θ =
, cosec θ =
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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Let x be the number of weeks; therefore, the two linear equations are
Where T stands for the punches on the tea punch card and C for the punches on the coffee punch card.
Solving by substitution. Set T=C, then
Thus, substitute the value of x=3 into the first equation,
Thus, after 3 weeks, Josiah will have the same number of punches on each card, and he will have 23 punches on each card.