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Sidana [21]
3 years ago
15

Based on Pythagorean identities, which equation is true? A. Sin^2 theta -1= cos^2 theta B. Sec^2 theta-tan^2 theta= -1 C. -cos^2

theta-1= sin^2 theta D. Cot^2 theta - csc^2 theta=-1
Mathematics
1 answer:
Arturiano [62]3 years ago
3 0

Answer:

D

Step-by-step explanation:

our basic Pythagorean identity is cos²(x) + sin²(x) = 1

we can derive the 2 other using the listed above.

1. (cos²(x) + sin²(x))/cos²(x) = 1/cos²(x)

1 + tan²(x) = sec²(x)

2.(cos²(x) + sin²(x))/sin²(x) = 1/sin²(x)

cot²(x) + 1 = csc²(x)

A. sin^2 theta -1= cos^2 theta

this is false

cos²(x) + sin²(x) = 1

isolating cos²(x)

cos²(x) = 1-sin²(x), not equal to sin²(x)-1

B. Sec^2 theta-tan^2 theta= -1

1 + tan²(x) = sec²(x)

sec²(x)-tan(x) = 1, not -1

false

C. -cos^2 theta-1= sin^2

cos²(x) + sin²(x) = 1

sin²(x) = 1-cos²(x), our 1 is positive not negative, so false

D. Cot^2 theta - csc^2 theta=-1

cot²(x) + 1 = csc²(x)

isolating 1

1 = csc²(x) - cot²(x)

multiplying both sides by -1

-1 = cot²(x) - csc²(x)

TRUE

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3 0
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Identify the translation of the figure with the vertices P(−4,−5), L(1,−7), and K(−9,8), along the vector &lt;−6, 3&gt;.
jarptica [38.1K]

Answer:

P ′(−10, −2), L ′(−5, −4), K ′(−15, 11)

Step-by-step explanation:

The translation vector, ⟨−6,3⟩, can be used to derive a rule for the translation of the coordinates: (x,y)→(x−6,y+3).

Apply the rule to translate each of the three preimage vertices to the image vertices.

P(−4,−5)→P'(−10,−2)

L(1,−7)→L'(−5,−4)

K(−9,8)→K'(−15,11)

Therefore, P'(−10,−2), L'(−5,−4), N'(−15,11) is the translation of the figure with the vertices P(−4,−5), L(1,−7), and K(−9,8), along the vector ⟨−6,3⟩.

4 0
2 years ago
Read 2 more answers
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