smc-4552-30-tan

Trigonometry, SMB-033 MC

If `tan theta = 80`, what is the value of `theta`, correct to 2 decimal places?

`5.40°`
`5.67°`
`89.20°`
`89.28°`

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`D`

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`tan theta`	`=80`
`theta`	`=tan^(-1)80`
	`=89.28°`

`=>D`

Trigonometry, SMB-031

Express the ratio of `tan theta` as a fraction. (2 marks)

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Hence or otherwise, find the value of `theta`, correct to two decimal places. (1 mark)

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`tan theta=15/8`
`61.93^@`

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i. `text{By Pythagoras,}`

`x^2+8^2`	`=17^2`
`x^2`	`=289-64`
	`=225`
`x`	`=15`

`:.tan theta = 15/8`

ii. `theta`	`=tan^{-1}(15/8)`
	`=61.927…^@`
	`=61.93^@\ text{(to 2 d.p.)}`

Trigonometry, SMB-030

Find the value of `theta`, correct to the nearest minute. (2 marks)

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`54^@ 28^{′}`

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`tan theta`	`=7/5`
`theta`	`=tan^{-1}(7/5)`
	`=54.462…`
	`=54^@ 27^{′}44^{″}`
	`=54^@ 28^{′}`

NOTE: Seconds > 30 are rounded up to the higher minute.

Trigonometry, SMB-029

Find the value of `theta`, correct to the nearest minute. (2 marks)

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`61^@ 56^{′}`

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`tan theta`	`=15/8`
`theta`	`=tan^{-1}(15/8)`
	`=61.927…`
	`=61^@55^{′}39^{″}`
	`=61^@ 56^{′}`

NOTE: Seconds > 30 round up to the higher minute.

Trigonometry, SMB-028

Find the value of `x`, correct to 1 decimal place. (2 marks)

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`3.0`

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`tan 68^@`	`=7.4/x`
`x`	`=7.4/(tan 68^@)`
	`=3.0\ \ text{(to 1 d.p.)}`

Trigonometry, SMB-027

Find the value of `x`, correct to 2 decimal places. (2 marks)

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`9.40`

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`tan 28^@`	`=5/x`
`x`	`=5/(tan28^@)`
	`=9.40\ \ text{(to 2 d.p.)}`

Trigonometry, SMB-026

Find the value of `x`, correct to 2 decimal places. (2 marks)

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`5.41`

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`tan 31^@`	`=x/9`
`x`	`=9 xx tan 31^@`
	`=5.4077…`
	`=5.41\ \ text{(to 2 d.p.)}`

Trigonometry, SMB-025

Find the value of `x`, correct to 1 decimal place. (2 marks)

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`28.0`

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`tan 70^@`	`=x/10.2`
`x`	`=10.2 xx tan 70^@`
	`=28.0\ \ text{(to 1 d.p.)}`

Trigonometry, SMB-024

Express `tan theta` as a fraction in its simplest form. (3 marks)

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`tan theta = (2sqrt5)/5`

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`text{Let unknown side =}\ x`

`text{By Pythagoras:}`

`6^2`	`=x^2 + 4^2`
`x^2`	`=36-16`
`x`	`=sqrt20\ \ (x>0)`

`:.tan theta`	`=4/sqrt20`
	`= 4/(2sqrt5) xx sqrt5/sqrt5`
	`= (2sqrt5)/5`

Trigonometry, SMB-023

Using Pythagoras and showing your working, express `tan 30^{@}` as a fraction. (2 marks)

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`tan 30^{@} = 1/sqrt3`

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`text{Let}\ \ x =\ text{unknown side}`

`text{By Pythagoras:}`

`2^2`	`=x^2 + 1^2`
`x^2`	`=4-1`
`x`	`=sqrt3\ \ (x>0)`

`tan 30^{@} = text{opp}/text{adj} = 1/sqrt3`

Trigonometry, SMB-003

Express the following as a fraction

`sin theta` (1 mark)

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`tan theta` (1 mark)

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`sin theta = 7/25`
`tan theta = 7/24`

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i. `sin theta = text{opp}/text{hyp} = 7/25`

ii. `tan theta = text{opp}/text{adj} = 7/24`

Trigonometry, SMB-002

Express the following as a simplified fraction

`cos theta` (1 mark)

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`tan theta` (1 mark)

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`cos theta = 3/5`
`tan theta = 4/3`

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i. `cos theta = text{adj}/text{hyp} = 6/10 = 3/5`

ii. `tan theta = text{opp}/text{adj} = 8/6 = 4/3`

Measurement, STD2 M6 2020 HSC 16

Consider the triangle shown.

Find the value of `theta`, correct to the nearest degree. (2 marks)

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Find the value of `x`, correct to one decimal place. (2 marks)

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`39^@`
`12.1 \ text{(to 1 d.p.)}`

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a.	`tan theta`	`= frac{8}{10}`
	`theta`	`= tan ^(-1) frac{8}{10}`
		`= 38.659…`
		`= 39^@ \ text{(nearest degree)}`

b. `text{Using Pythagoras:}`

`x`	`= sqrt{8^2 + 10^2}`
	`= 12.806…`
	`= 12.8 \ \ text{(to 1 d.p.)}`