Match equivalent trigonometric ratios.

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cosθ

sinθ

cotθ

secθ

cscθ

tanθ

csc (90° - θ)
sin (90° - θ)
tan (90° - θ)
cos (90° - θ)
cot (90° - θ)
sec (90° - θ)

Hello from MrBillDoesMath!

csc (90° – x) = sec (x )

sin (90° – x) = cos (x )

tan (90° – x) = cot (x)

cos (90° – x) = sin (x )

cot (90° – x) = tan (x )

sec (90° – x) = csc (x)  

Thank you,

MrB    

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)