Give the equation of the graph pictured below
2 answers:
Now, if you notice the picture below
the amplitude of the graph we have above, is squished by half, what in sin(θ) would be an amplitude of 1 above the red midline and 1 below it, for the graph above became 1/2 above the midline and 1/2 below it, for an amplitude of 1/2
now, sin(θ) starts off from 0 and goes up then down, now, if you simply give it a negative leading coefficient, the graph will flip upside-down, or -1/2
if we look at the period of the graph above, is 2π, and the period of sin(θ) is also 2π, so, no change on the period
but the graph above is shifted, from a midline at y = 0, to y = -2, so it has a vertical shift of -2
thus
the amplitude of the graph we have above, is squished by half, what in sin(θ) would be an amplitude of 1 above the red midline and 1 below it, for the graph above became 1/2 above the midline and 1/2 below it, for an amplitude of 1/2
now, sin(θ) starts off from 0 and goes up then down, now, if you simply give it a negative leading coefficient, the graph will flip upside-down, or -1/2
if we look at the period of the graph above, is 2π, and the period of sin(θ) is also 2π, so, no change on the period
but the graph above is shifted, from a midline at y = 0, to y = -2, so it has a vertical shift of -2
thus
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See the picture attached.
We know:
NM // XZ
NY = transversal line
∠YXZ ≡ ∠YNM
1) <span>We know that ∠XYZ is congruent to ∠NYM by the reflexive property.</span>
The reflexive property states that any shape is congruent to itself.
∠NYM is just a different way to call ∠XYZ using different vertexes, but the sides composing the two angles are the same.
Hence, ∠XYZ ≡ <span>∠NYM</span> by the reflexive property.
2) Δ<span>XYZ is similar to ΔNYM by the AA (angle-angle) similarity theorem
The AA similarity theorem states that if two triangles have a pair of corresponding angles congruent, then the two triangles are similar.
Consider </span>Δ<span>XYZ and ΔNYM:
</span>∠YXZ ≡ <span>∠YNM
</span>∠XYZ ≡ ∠NYM
Hence, ΔXYZ is similar to ΔNYM by the AA similarity theorem.
We know:
NM // XZ
NY = transversal line
∠YXZ ≡ ∠YNM
1) <span>We know that ∠XYZ is congruent to ∠NYM by the reflexive property.</span>
The reflexive property states that any shape is congruent to itself.
∠NYM is just a different way to call ∠XYZ using different vertexes, but the sides composing the two angles are the same.
Hence, ∠XYZ ≡ <span>∠NYM</span> by the reflexive property.
2) Δ<span>XYZ is similar to ΔNYM by the AA (angle-angle) similarity theorem
The AA similarity theorem states that if two triangles have a pair of corresponding angles congruent, then the two triangles are similar.
Consider </span>Δ<span>XYZ and ΔNYM:
</span>∠YXZ ≡ <span>∠YNM
</span>∠XYZ ≡ ∠NYM
Hence, ΔXYZ is similar to ΔNYM by the AA similarity theorem.